To: Distribution
From: David K. Kahaner, ONR Asia [kahaner@xroads.cc.u-tokyo.ac.jp]
      Stephen G. Nash, George Mason Univ [snash@gmuvax.bitnet]
Re: 2nd Int Conf on Numer Optimizat & Applica, Xi'an China, June 24--27, 1991
21 August 1991                                                           
This file is named "xian.rpt"

ABSTRACT. A summary of the Second International Conference on Numerical 
Optimization And its Applications, Xi'an Jiaotong University, Xi'an, 
China, June 24--27, 1991. Also a description of visits to the computing 
center at the Chinese Academy of Sciences (Beijing), and to Fudan 
University (Shanghai).  

There may be some updates to this report, as I am still waiting for
Chinese input. (DKK)

INTRODUCTION.
The authors attended the Second International Conference on Numerical 
Optimization And its Applications, Xi'an Jiaotong University, Xi'an, 
China, June 24--27, 1991, where Nash gave a contributed paper. Kahaner 
and Nash gave lectures at Fudan University in Shanghai.  Kahaner lectured 
at the computing center at the Chinese Academy of Sciences in Beijing.  
These visits are described below. A full list of the titles and authors 
of papers given at the Xi'an conference, as well as from representative 
issues of the Chinese Journal of Engineering Mathematics are appended to 
the end of this report.  

XIAN, BACKGROUND.
This was the second in a proposed series of conferences on optimization.
The first was held in 1986, also at Xi'an Jiaotong University. 
The host was 
        Prof Zhaoyong You
        Institute for Computational and Applied Mathematics
        Xi'an Jiaotong University
        Xi'an, Shaanxi 710049
        PRC
         Tel: 86-29-335011, ext 744, Fax: 86-29-335471
who has recently celebrated his 60th birthday. (The June 1991, Chinese J 
Eng Math, Vol 3 #2 is dedicated to this event. Most of the papers are 
given in English; the titles and authors are attached to this report to 
illustrate the flavor of the basic research.)  The entire staff of the 
Institute, especially Dr. Chengxian Xu, worked extraordinarily hard to 
satisfy the requirements of the Western attendees and their families.  

Xi'an Jiaotong University is one of about half a dozen in China (and one 
in Taiwan) with the name Jiaotong (meaning "transportation", or
"commerce"). The first was founded in Shanghai in 1896, and the Xi'an
campus was opened in 1956. It is a university with a main focus on
natural science and engineering, and secondarily on liberal arts and
management. Student enrollment in Xi'an is about 12,000 including 2200
graduate students. There are over 2400 faculty including more than 750
at professor or associate professor level. About 250 foreign students
are on campus from Canada, France, Germany, Japan, the Netherlands,
Poland, Switzerland, UK, US, and Hong Kong. Plans are to increase
enrollment to 15,000 in the next few years with a corresponding staff
increase.

Its campus was heavily treed, spacious, and attractive. There were a 
number of lovely gardens and fountains, and it was generally an enjoyable 
place to stroll. University buildings appeared to vary from brand new to 
1950's vintage, and all seemed in good condition as far as we could tell.  
One Western attendee elected to stay at the university guest house, while 
the others chose an international hotel a short distance away.  The guest 
house appeared to be perfectly satisfactory but lacked the ambience of 
the hotel.  

(We should mention in passing for those who have not been to China, that 
first class accommodations were available every place we visited.  
Western hotels such as Hyatt, Holiday Inn and Sheraton are common and 
provide a level of service--and price--essentially equivalent to that in 
other countries. Of course, less expensive hotels are also widely 
available.  But there is a discontinuity between the luxury in these 
hotels and the facilities used by working Chinese; this was very 
noticeable in Xi'an.  Also, international hotels use a special currency 
that can only be obtained when visitors exchange foreign currency, and 
hence is not normally available to Chinese.  Nevertheless, all the 
visitors to this conference were impressed with the fact that people on 
the streets looked, if not prosperous, at least well clothed and fed. In
fact, one returning visitor remarked at how much improvement there had
been since his last visit.)

Although we walked around the campus, there was no opportunity for a real 
tour. This was disappointing, as the campus literature lists a 1.4M 
volume library with 8K journals, several university-owned factories 
(Machine Manufacturing, Electronic Devices, Computer Manufacturing, 
Research and Teaching Facilities), 62 laboratories (including Structural 
Strength and Vibration, Metallic Strength and Vibration, Image 
Processing, Two-Phase Flow, Lubrication and Bearing, Computer Systems and 
Applications, Natural Dialectrics, etc.), engineering departments 
(Mechanical, Energy and Power, Power Machinery, Electrical, Information 
and Control, Computer Science/Eng., Materials Science, Chemical) as well 
as Physics, Engineering Mechanics, Architecture/Structural Engineering, 
Mathematics, Mechanology (machine design and manufacture), Social 
Sciences, etc. We were told that Xi'an has academic exchange agreements 
with almost thirty other universities including 10 in the US and 6 in the 
UK, but we had no opportunity to meet any visiting scholars. The city of 
Xi'an has recently become internationally famous because of the 
discovery, in 1974, of many thousands of ancient life-sized terra-cotta 
warriors. This site, and the enormous activity surrounding it, are really 
wonders of the world. Visiting conference attendees always want to see 
these, and conference organizers now build such a trip into the schedule.  
We feel that it would also be useful to allow time within the scientific 
program for a careful university tour, and in fact there appeared to be 
ample slack time within the program for this.   

There is a serious language problem confronting Chinese scientists who 
wish to communicate in English. The Western attendees all agreed that 
many potentially interesting talks were almost impossible to follow, 
although it was clear that the Chinese speakers had prepared carefully.  
In fact, many scientists actually read their papers and yet some of these 
were among the most difficult to understand. The printed papers that were 
available to us were acceptable, but a large fraction would still be 
rejected for publication in critical journals.  In a perfect world we 
would hope that Western scholars would be willing to go half-way and 
learn a little Chinese, but in reality the language of science--
especially computation, is English and the Chinese need to continue 
working to improve their skills. The Western attendees also felt that, 
language issues aside, the Chinese need to spend more time training their 
younger scientists on the mechanics of lecturing, especially with 
transparencies. We often forget that presentation skills that are taken 
for granted in the West, need to be learned somewhere. The university has 
a department of foreign languages and has specialized courses in English 
(and Japanese) for Science and Technology, but perhaps science students 
do not have much opportunity to participate in these. Perhaps senior 
Chinese scientists could coach their younger colleagues. Also, in the 
West we have many excellent and experienced speakers, and we suggest, 
respectfully, that a few simple lectures on "How to give a lecture to a 
Western audience" presented by well known Western scientists during their 
visits to China would be very helpful in improving information flow 
between the countries.  (Needless to say there are many Western scholars 
who could also profit by attending such lectures.) 
  
The lectures were held in a building that was nearly new, in one medium 
sized lecture room and two small classrooms. The latter had rather poor 
overhead projectors. This caused a real problem, as the combination of 
badly focusing equipment and extremely flimsy transparencies made a 
number of the Chinese talks even more difficult to follow. Actually, 
transparencies are very expensive and it is not surprising that they are 
used economically, but perhaps it would have been better to shave the 
budget in some other areas instead.  Surprisingly, the building also had 
a spectacular lecture hall that would have been perfect, but for some 
reason was not used.  

TOPIC OF THE CONFERENCE.
Numerical optimization has many applications throughout the applied 
sciences, as well as in numerous business and military applications.  It 
has been an especially active research area in recent years because of 
the success of interior point methods in linear programming.  This 
conference aimed to "further these developments by bringing together the 
chief numerical analysts, applied mathematicians, operations researchers, 
computer scientists and engineers with interests in numerical 
optimization and its applications from around the world to share their 
work." 

In the preliminary program it was announced that there would be five 
invited talks (two from the People's Republic of China, one from Taiwan, 
one from Germany, and one from Canada) as well as 93 contributed papers 
(most from China).  There were a substantial number of changes to the 
final program regarding the contributed papers.  Revised schedules were 
produced each morning, but even so, there were gaps in the program due to 
last minute withdrawals, absences, or "no-shows" (by both foreign and 
Chinese speakers).  Foreigners at the conference included one from 
Taiwan, one from Germany, one from New Zealand, one from Spain, four from 
Italy, one from Canada, and four from the U.S.A. Among those who were 
absent were scientists from the Soviet Union, Iran, and from Vietnam.  
The conference was run in English, corresponding to its designation as an 
international meeting.  Cash prizes were awarded for the best three 
papers by young Chinese researchers, although the third prize was split 
between two papers. Prizes were decided by a committee consisting of 
three Chinese, plus L.R. Foulds (New Zealand), W.J.  Gilbert (Canada), 
and chaired by G. Alefeld (Germany).  

Prizes were as follows.

First prize:  Huang Zhijan, On the Convergence of the Brent Method (joint 
                  work with Wang Deren).  

Second prize: Wei Bin, A Class of Reduced Gradient Methods for Nonlinear 
                  Programming Problems With Linear Constraints (joint 
                  work with Xu Chengxia 

Third prize: (split)
              Xu Xiaojie: On the Implementation of Interior-point Methods 
                  for Linear Programming 
              Xu Chen: Modelling of Flexible Robot Dynamics With Optimal 
                  Shape Functions.  

A complete list of the presentations is supplied as an appendix to this 
report. (The large number of program changes means that our list of 
papers might not be completely accurate.) Because the contributed papers 
were sometimes presented in three parallel sessions, we were not able to 
hear all the talks at the meeting.  The information below is based on the 
talks that we attended, and the general comments (both those earlier and 
just below) seemed to be shared by all the Western attendees.  

Many of the talks were outside the mainstream of optimization algorithms 
and applications as viewed from the West. The algorithmic topics often 
seemed old fashioned, and the applications topics esoteric by Western 
academic standards. There are a number of possible explanations.  

(1) The references in the papers were often to years-old papers in 
Western journals, perhaps indicating a difficulty of obtaining journals 
(although, see the discussion of Fudan University below).  

(2) The algorithmic research in China is severely constricted by the lack 
of computing equipment.  Some universities have virtually no equipment, 
while others only have a limited number of small machines (such as IBM 
PCs, XTs, and ATs, and their equivalents). There was evidence that a 
small number universities had parallel computers including at least a few 
Western machines, such as ELXSI (now defunct), but none of the papers 
that we heard at the conference, nor any of the individuals we spoke to, 
made use of these machines. Thus, there is a natural tendency to "make-
do" and adjust techniques and problems to those that can be handled on 
small machines, or perhaps just pencil and paper. Not surprisingly, there 
is a great deal of theoretical research and analysis and much less 
emphasis on experimental computation.

(3) The applications that were described were frequently connected with 
Chinese manufacturing, transportation, or distribution problems, and as 
with computing equipment, in China many of these are not as sophisticated 
as in the West; this sometimes led to what seemed to be unusual 
assumptions in the models that were being used.  Although we have seen a 
large amount of very excellent theoretical research from Chinese 
scholars, a heavy emphasis in the Chinese papers presented at this 
conference were on very direct and practical applications, optimization 
of helicopter rotor blade design, electrical power loading, shape of 
bellows, river pollution control. This is related to the focus in Chinese 
research on using technology to solve the many serious problems 
confronting the country. In the West, academic researchers tend to be 
much more interested in developing new techniques than in applying 
existing ones (even if very creatively) to specific problems.  

There was an intense curiosity among the Chinese researchers about work 
in the West. Many of the talks demonstrated that these researchers have 
considerable technical and analytic skills, but lack library and 
computing resources to support these skills, or at least that 
communication between the research staff and these resources is weak and 
needs to be strengthened.  

CONFERENCE PRESENTATIONS
What follows are notes on some of the talks that we attended.  Not all 
talks are mentioned since in many cases the abstracts in the conference 
program provide adequate descriptions of the content of the talks. (We 
will make a copy of abstracts available to requestors.) Speakers are from 
China unless otherwise noted.  

Goetz Alefeld (Germany)---Recent results for the interval-arithmetic 
version of Newton's method.  An analysis of the divergence (failure) of 
Newton's method when interval arithmetic is used.  

Shen Zuhe---Interval-majorant method for global optimization and its 
applications.  A review of various theoretical results and algorithms for 
global optimization was given.  These were extended to the setting of 
interval arithmetic and the results were applied to a mini-max problem.  

Massimo Gastaldi and Agostino la Bella (Italy)---Optimal growth in a 
multiregional and multisectoral economy.  An attempt to reduce regional 
disparities in the Italian economy through optimization methods and 
models. They presented a multi-regional and multi-sectoral dynamic model.  
There were deficiencies in the pure model (e.g., lack of data), and 
optimal control techniques were used to remedy these deficiencies.  
Solutions were then obtained by dynamic programming, using discretization 
in the time variable.  

Sergio Barba-Romero (Spain)---Nonlinear optimization models for the new 
Spanish Autonomous Communities financing system.  Starting with a basic 
linear programming model, quadratic constraints and objective terms were 
added, with the possibility of additional cubic constraints if the 
original augmented model was inadequate.  The problems were solved using 
GINO on a micro-processor (the problems had 37 variables and 32 
constraints).  

Li Naicheng and Zhang Kecun---Parameter optimization method for problems 
of elastic fluids.  Solving lubrication problems via nonlinear parametric 
programming, based on an ODE boundary-value problem.  A guess is made for 
a pressure curve p(x) (a parametric model), and then a least-squares 
objective function is used to get a solution.  In this talk p(x) was a 
spline.  Numerical solutions were obtained.  

Li Yiping---Cubic potential for strictly nonlinear oscillators.  A series 
expansion was used to cope with two different time scales in the problem.  
An analytic solution was obtained for the case of a cubic potential, and 
the author considered cubic approximations to more complex potentials.  

Li Pingyuan, Pan Xiaoqin and Ding Peyong---On the corresponding points of 
contact, line of contact and velocity ratio of two quadratic arcs which 
are best approximations in involute profiles.  This talk was concerned 
with the manufacture of gears.  Various assumptions and restrictions were 
imposed, apparently because of the limitations of Chinese gear-
manufacturing equipment.  

Feng Chengmin (Taiwan)---Multi-objective optimization, theory and 
application.  This was a survey of basic ideas in this area.  There were 
several other papers on multi-objective optimization presented at this 
conference. The topic is of considerable interest in China, and there 
will be a conference in Taipei, Taiwan (Tenth International Conference on 
Multiple Criteria Decision Making) 19-24 July 1992, at National Chiao 
Tung University, 4F 114 Sec 1, Chung-Hsiao W. Rd., Taipei 100 Taiwan, 
ROC.  

W. J. Gilbert (Canada)---Newton's iteration method and its 
generalization.  The speaker looked at generalizations of Newton's method 
for solving f(x)=0.  The generalizations included (a) variants for 
multiple roots, (b) higher-order methods, (c) the secant method, and (d) 
Steffenson's method.  Julia sets associated with the convergence of these 
methods were illustrated for various polynomial examples in one variable.  

S. S. Oren (USA)---Optimal pricing of delivery priority and spec levels 
for semiconductor products.  The speaker developed a model for setting 
prices of custom VLSI chips.  The formulation was a nonlinear programming 
problem.  The model was based on the fact that chips are not uniform 
(they vary in speed, for example), but this cannot be determined until 
after manufacture.  

Dorit Hochbaum (USA)---The empirical performance of a polynomial 
algorithm for constrained nonlinear optimization.  The speaker considered 
a nonlinear programming problem with a separable, convex objective 
function and linear inequality constraints.  Some complexity results were 
derived based on a discretization of the variables in a bounded interval.  

Yue Ming---Cone duality theorem of semi-infinite programming problem and 
relative algorithm.  The speaker considered a semi-infinite linear 
programming problem, where all the points must lie in a closed convex 
cone.  The dual problem was derived.  Under strong assumptions, some 
further results were derived in the nonlinear case.  

Stephen G. Nash and Ariela Sofer (USA)---A general purpose parallel
algorithm for unconstrained optimization.

Gao Li--An Algorithm for One-sided Huber Optimization with Applications 
to Circuit Design Centering. Huber optimization is a combination of L-1 
and L-2 optimization which seems particularly useful in those cases where 
the sign of the error at the data values is important. The basic 
algorithm also switches between a trust-region Gauss Newton method and a 
Quasi-Newton method.  

Wang Shiding--Research on optimal long term scheduling of an irrigation-
electric power reserovoir. There are over 85,000 reserovoirs in China. 
Using an lp model the author claims to have been able to increase total 
electrical output 4-5% along one particular river.  

Tian Fengwei---A new algorithm for optimal streamflow regulation of 
cascade hydro reservior systems. A combination of well known methods, but 
the application was claimed to improve output about 7% along one river.  

Tian Zhiyuan---Convergence of simplex method for two-variable functions.  
This title refers to the Nelder-Mead direct search method for 
unconstrained nonlinear minimization.  Convergence was established for 
certain two-variable problems.  

Yang Boting---The software package of optimum design for valve gear 
mechanism of internal combustion engines. This paper describes a software 
package for Cyber machines, of more than 10000 lines of Fortran-77.  The 
speaker presented many numerical results indicating that the software 
accurately models this complex system. It was very difficult to determine 
the actual optimization methods that were in use, but if the results are 
valid this package might be of practical interest in the automotive 
industry.  

Hu Xinsheng---Complementarity problem of set functions and its 
application in nondifferentiable optimization. Some theoretical results 
on set-valued functions. The results were applied to non-smooth 
optimization problems, with computational results on an IBM PC.  

F. Facchinei and S. Lucidi (Italy)---On the solution of simple 
constrained optimization problems by an exact penalty approach.  The 
authors considered the problem of minimizing a nonlinear function subject 
to either (a) bounds constraints, or (b) non-negativity constraints plus 
the restriction that the variables sum to unity.  This was solved via an 
augmented Lagrangian approach (i.e., using a differentiable exact penalty 
function).  

Fu Li---The approximating exact penalty function method.  An exact 
penalty function was derived using general norms for the penalty terms.  

Pen Benchen---The application of optimum method in wing structure D-
design of airplane. This was a very brief introduction to a software 
system (over 70K lines) developed since the late 1970's.  

Guo Dinghe and Zhang Kecun---Numerical method for conditional variational 
problem with double objectives.  This talk was concerned with the design 
of a lens.  Two objective terms were used to control spherical and 
chromatic aberration.  The problem was solved via parametric programming.  


FINAL COMMENT. Meetings such as this, held in far away and exotic places, 
have a special fascination to Westerners. But with language, culture, 
climate, and time differences, participating in them is plain hard work, 
and sometimes the scientific rewards are not obvious at first.  
Nevertheless, visiting attendees are important to their hosts and hence 
have a significant responsibility to them and to their scientific peers.  
This responsibility is best discharged by active participation and 
attendance.  Professor Goetz Alefeld (Germany) deserves special 
commendation; he was in constant attendance and provided almost non-stop 
encouragement and suggestions to younger Chinese scientists. We also 
think that US funding agencies should ask for full accounting from 
Western attendees, intellectual as well as financial.  


FUDAN UNIVERSITY, SHANGHAI.  
On July 3 Kahaner and Nash visited Fudan University in Shanghai.  Their 
host was 
        Professor Erxiong Jiang
        Chairman and Professor of Department of Mathematics
        Fudan University, Shanghai PRC
          Tel: 5491427, Fax: 5453039
although he was not at Fudan on the day of their visit (Kahaner met Prof 
Jiang the day before in Beijing at the Academy of Science). Instead, they 
were escorted by Prof Cao Zhi-Hao, also in the Math department at Fudan.  

Shanghai is said to be the industrial heart of China, comparable to 
Chicago in the US. It was certainly highly industrialized and crowded.  
Our visit coincided with several weeks of heavy rains and the resulting 
serious flooding, so most of our movements were restricted.  

We had both been asked to give lectures, and then were shown around the 
University.  This was between sessions, and the campus had the typical 
look associated with that period everywhere in the world.  Our original 
plan was to spend the afternoon and evening with university staff, but 
weather problems curtailed this, and we had much less interaction than we 
would have liked. The lectures were primarily attended by about 15-20 
students, who characteristically, had very few questions. There was also 
a serious language problem. By now, Kahaner has a reasonable amount of 
experience giving lectures in English to non-native speakers, but he felt 
that a large fraction of the lecture content was lost. And generally, he 
believes that the level of English knowledge in China is much lower than 
in Japan, even among relatively well traveled senior scientists. In fact, 
we were told that senior (hence older) scientists are more likely to be 
comfortable speaking Russian than English.  

A short campus tour included the Mathematics Library, and the Computing 
Center.  The Library had an extensive collection of journals and books, 
both Chinese and foreign.  Although some of the foreign journals were 
originals, most were reproductions including copies of SIAM, ACM, IEEE, 
Elsevier, and others.  We were told that there is insufficient funding to 
purchase these journals for all the universities at international foreign 
exchange rates. Instead, one subscription is purchased by the Chinese 
government, and this is then used for widespread copying.  At the time we 
examined library shelves (7/91), these copied journals were well stocked 
through the end of 1990.  We were also told that some original journal 
issues were provided by professors who are on journal editorial boards 
and receive free subscriptions.  The collection of foreign books, 
however, appeared to consist exclusively of originals.  There was 
evidence that many new books were entering the library, consisting of 
typical research monographs that one would expect in such a library, but 
also some more unusual titles (Statistics for Lawyers) that are 
surprising given the stated tight budgets.  

We were interested in the issue of journals because it related directly 
to intellectual property rights (IPR) and also to every scientist's 
desire for full and free flow of information.  There are various 
perspectives on protection of intellectual property, with some claiming 
that socialist enterprises shouldn't adopt patents, or that patent laws 
would mostly benefit foreigners because there were fewer inventions in 
China. These worries have proved unnecessary and China is striving to 
improve IPR. However, there are several departments charged with patent, 
trademark and copyright protection in China, and this slows down any 
changes.  Even with new laws concerning IPR, violation of property rights 
is still common.  Tang Zongshun, consultant to the State Council and 
vice-chairman of the China branch of the International Association for 
Intellectual Property Protection, feels the key question is how to 
enforce and coordinate existing laws effectively.  

We asked two ex-Presidents of SIAM their opinions on journal copying.
Here are their personal opinions.

Prof Gene Golub (Stanford):
"The problem of exchanging journals with third world countries has 
plagued us for some time. I don't know what to do at this time but we 
shouldn't be passive and do nothing. The only thing I can think of is to 
publish some international journals and then use the profits for sending 
journals. Does the American Mathematical Society have any policy? Here's 
a place where the mathematical societies might cooperate.  I think 
there's a real need to begin to communicate with third world 
organizations. Perhaps this can only be done through governmental
channels."

Dr. Bill Gear (Formerly U-Illinois, now NEC):
"At the moment individuals in countries with the economic situation of 
China cannot afford to subscribe to journals such as those of SIAM, even 
if we reduced the costs to the point we were losing money on each copy.  
Unless the membership expressed a strong interest in proving significant 
economic support to scientists in other countries, it seems to me that 
the officers fiduciary responsibilities to members do not permit them to 
subsidize particular groups in a major way.  On the other hand, I suspect 
that most members would want to be as helpful as possible to individual 
scientists and give them access to international scientific publications.  
Thus, while a country is in a state such that there is no prospect for 
its scientists to get journals any other way, I personally would not want 
to see pressure mounted to stop the process of reproducing journals 
internally for distribution to libraries. I imagine that the PRC 
government can produce copies far less expensively than we can in the US.  
However, I would like to see agreements concerning such distribution.  
These should specify the extent to which distribution is permitted, and 
some payment to offset the costs of production of the original.  Any 
distribution outside of the country should be banned.  Payments could be 
based on the economic situation in the country and be renegotiated from 
time to time." 

Fudan University has a Computing Center, and we were taken on a tour by 
Professor Chen Jing Hai, who is its Director. He led us to understand 
that this resource is not made available to all departments of the 
University. Instead, it is associated with the Computer Science 
Department, and the Mathematics Department does not seem to have ready 
access to the equipment.  The equipment includes dozens of personal 
computers (IBM PCs, XTs, and ATs, as well as the Chinese Great Wall 
equivalents), an older Honeywell mainframe, a Hewlett-Packard mini-
computer, as well as terminals, tape and disk drives, and printers.  
There were one or two Unix workstations. We were not shown any examples 
of the projects that researchers at the University were engaged in.  
Also, the center was not in wide use the day we visited, but this could 
be because it was summer and classes were not in session.  


COMPUTING CENTER, ACADEMY OF SCIENCE
Kahaner visited here on 2 July. His host was
        Prof Zhong-ci Shi
        Prof of Mathematics and Director of the Computing Center
        Academia Sinica
        P.O. Box 2719
        Beijing China (PRC)
          Tel: +86-1-283967 (O), 1-2562192 (H), Fax: 1-2562485
          Email: BMAACC@ICA.BEIJING.CANET.CN
Professor Shi is also the Vice-President of the Chinese Mathematical 
Society, and the Head of the National Laboratory of Scientific and 
Engineering Computing. He and Kahaner met at an international conference 
in Japan in 1990. Shi is well known for his work on analysis of finite 
element methods for partial differential equations, although this is 
highly theoretical.  He has traveled widely, and in fact was leaving soon 
after for a SIAM meeting in Washington DC. He is also responsible for 
general purpose computing at the Chinese Academy of Science, (CAS), which 
is in reality a large collection of research institutes. Shi told me that 
there are about 80,000 students and researchers in and around Beijing at 
institutes and universities.  

The CAS computer center is about 25 years old, and not only encompasses 
the computers but also almost 500 staff, including more than 300 
researchers and technicians of which about 100 are equivalent to either 
full or associate professor level. Thus the center not only provides 
computer service but also performs teaching and research in computational 
mathematics, applications, computer science, networking, Chinese 
character processing, etc. In addition, it is also responsible for the 
establishment of a scientific database system which is considered a 
national key project. This involves work on about 20 scientific databases 
in chemistry, physics, biology, geography, etc., which will eventually be 
implemented on a large distributed system.  About 15 masters and 10 PhD 
students are admitted each year, and there are also a few post-docs.  

Hardware at the center is currently based on two IBM mainframes, a 4341 
and 4361. Prof Shi explained to me that the actual computer center was 
shut down because various rooms were being moved, and about the only 
computer related material Kahaner saw was a large stack of floor panels. 
But several Convex C120 systems have recently been sold to China, so it 
is a good bet that one of them will be installed here.  

Shi explained that there are a number of major research projects,
oriented around 
  Mathematical physics (Hamiltonian systems--see below, fluid mechanics, 
     quantum chemistry, structural analysis, seismic exploration) 
  Numerical solution of partial differential equations (finite element, 
     variational, multi-grid, and boundary element methods) 
  Software for science, engineering and statistics
  Optimization (interior point and trust region methods)
  Inverse problems
  Computational geometry
  Computer algebra for cryptography
  Chinese character I/O
  Parallel algorithms
  Fourth generation computer languages
as well as some unusual projects such as Lie algebras and numerical 
methods for pharmacology. There are also several journals including 
"Journal of Computational Mathematics" (in English), and an English 
translation of "Chinese Journal of Numerical Mathematics and 
Applications." 

Kahaner was particularly interested in available scientific software. The 
center subscribes to IMSL (US) and NAG (UK) and also has its own library 
in mathematics (STYR), statistics (SASD), and computational physics 
(CPS). For example, STYR, which is the responsibility of Cui Fun-Zhi 
(Tel: 256-3753) at the same address as Shi, has over 300 user callable 
modules (almost 700 modules total) written in Fortran-77 and made 
available on PCs under DOS, Unix, and OS/2 as well as the center's 
mainframes in the following categories.  
   Special functions
   FFT
   Splines
   Quadrature (1D and multiple)
   Eigenvalues and eigenvectors
   Nonlinear equations
   Least squares
   Roots
   Linear and nonlinear programming
   Optimization (constrained and unconstrained)
   Ordinary differential equations
   Matrix and vector computation
   Graphics, including surfaces
   Machine parameters and error handling
Thus it looks to be functionally similar to large software collections in 
the West, such as the SLATEC library which is used at the major DOE 
laboratories and other places. Kahaner was told that several Japanese 
scientists collaborated on this work, and it has some relationship to the 
NUMPAC project from Nagoya and Chubu Universities.  

Also at the Academy was
        Prof Kang Feng
        Honorary Director, Academia Sinica Computing Center
        P.O. Box 2719
        Beijing China (PRC)
          Tel: +86-1-289001 (O), 1-285203 (H)
Professor Feng is also  President, Chinese Society of Computational 
Mathematics. Since the early 1960s he has been interested in Hamiltonian 
dynamics. By that we mean the description of the motion of an n-degree of 
freedom system by use of the 2n ordinary differential equations 
describing the first partials of the system's Hamiltonian. The 
geometrization of these ideas, developed by Poincare, has been named 
"symplectic geometry". Virtually all real physical systems with 
negligible dissipation can be cast, somehow, into Hamiltonian form, and 
Feng and his collaborators are convinced that this is a fruitful starting 
point for development of numerical methods. They have a substantial 
collection of papers (in English) describing the ideas, and a few in 
which symplectic Runge-Kutta and leap-frog schemes are used to integrate 
the nonlinear oscillator and even more difficult systems, with excellent 
results over long-times. Kahaner was not aware of this work before. It is 
really excellent and deserves to be much better known in the West. One 
accessible reference is the following.  
   "Hamiltonian algorithms for Hamiltonian systems and a comparative 
    numerical study", Feng Kang & Qin Meng-shzo, in Computer Physics 
    Communications, Vol 65 (1991) pp173-187.  

Feng was also very interested in Japanese research on parallel computing.  
Kahaner was not made aware of any Chinese work on parallel computation, 
except of a very theoretical nature, and feels that this mostly stems 
from lack of access to suitable platforms. Chinese scientists are aware 
that they are far behind in this area, and that there is a substantial 
"spin-up cost" that they will eventually have to pay. The few Chinese 
parallel processing projects we read about are either based on transputer 
systems that researchers are configuring themselves, or on old ELXSI 
hardware.  Lack of electronic networks prevents remotely-based 
researchers from accessing even these systems.  

One of the most interesting aspects of this part of the visit was the 
fact that some Chinese institutions ARE beginning to have electronic 
mail.  This is still in a very undeveloped state compared to Western 
countries, but as all of us who use this kind of communication know, it 
is an essential ingredient in timely information flow. For many it would 
be difficult to imagine life without email.  

------------------------------------------------------------------------

THE 2ND INTERNATIONAL CONFERENCE ON NUMERICAL OPTIMIZATION AND ITS
APPLICATIONS

Sponsored by National Natural Science Foundation of China (June 24-27, 1991)

An Improvement of Kachiyan's Algorithm for Linear Programming
     Cao Jiaming (South-west Jiaotong University, China)

Stochastic Neural Nets, Information and Optimization
     Caro Lucas (Tehran University, Iran)

Interactive Optimization and Fuzzy Analytic Hierarchy Process for
Multicriterion Water Resources Development
     Chang Caie, Wang Shiding (Shaanxi Institute of Mechanical Engineering,
     China)

Applications of Methods of Fuzzy Mathematics and Operations Research in 
Economic Scheduling of Hydro-Thermal Power Systems
     Duan Yu Rong, Wang Yong, Yang Dan (Chongqing Univ)
     Yang Mao Yuan, Wang Ping (Southwest Power Admin Bureau, Ministry of 
     Electric Power Industry)

Multiobjective Optimization - Theory and Application
     Cheng-Min Feng (Institute of Traffic and Transpiration, National Chiao
     Tung University, Hsinchu, Taiwan)

Constrained Functional Minimization in Data Fitting
     Cheng Ping, Zhang Kecun (Xi'an Jiaotong University, China)

Optimal Methods Used in the Design of U-shaped Expansion Bellows
     Chen Yifeng, Xu Jingan (Research Institute of Chemical Industry Machine,
     China)
     Xu Chengxian, Zhao Yingliang (Xi'an Jiaotong University)

A Connected m-tree Relaxation for m-Travelling Salesmen Problems
     Chung-Hsing Huang (College of Management, Taiwan University)
     Jiin-Chung Huang (College of Management, Taiwan University)

The Interactive Goal Programming Method on Evaluating the Quality for Graduate
Education
     Dai Hong, Deng Renming, Chen Jiajian (Chongqing University)

An Application of Multiobjective Decision Making for Optimal Load Dispatch of
Electrical Power System in City
     Deng Renming, Dai Hong, Chen Jiajian (Chongqing University)

Interior Point Algorithms and Dynamic System
     Diao Zaiyun (Shandong University, China)

On a Linear Program in the Space of Borel Measures and Applications
     Dinh Dung (Institute of Computer Science, Vietnam)

Optimal Growth in a Multiregional and Multisectoral Economy
     Domenico Campisi, Massimo Gastaldi (Instituto di Analisi dei Sistemi ed
     Informatica del CNR, Italy)
     Agostino La Bella (Universita degli Staudi di Cassino, Italy)

The Empirical Performance of a Polynomial Algorithm for Constrained Nonlinear
Optimization
     Dorit S. Hochbaum (University of California, U.S.A.)

An Adaptive Clustering Algorithm for Global Optimization
     Fabio Schoen (Dept. of Computer Sciences, University of Milano, Italy)

On the Solution of Simple Constrained Optimization Problems by an Exact
Penalty Approach
     Facchinei F. (Universita di Roma "La Sapienza", Italy)
     S. Lucidi (Instituto di Analisi dei Sistemi ed Informatical del CNR,
     Italy)

A Facilities Layout Decision Support System
     Foulds L.R. (University of Waikato, New Zealand)

The Approximating Exact Penalty Function Method
     Fu Li (Chongqing University, China)

An Optimization Policy of Dynamic Design for Helicopter Rotor Blade
     Gao Fuan, Yu Xijian (Chinese Aeronautical Computation Technique Research
     Institute, Xi'an, China)

An Algorithm for One-sided Huber Optimization with Applications to Circuit
Design Centering
     Gao Li (Department of Mathematics, Peking University, China)

Recent Results for the Interval-Arithmetic Version of Newton's Method
     Goetz Alefeld (Univ. Karlsruhe, Germany)

Sub-linear Programming Method for Linear Programming
     Gong Daping, Xu Shurong (Zhongshan Univ., China)

Numerical Method for Conditional Variational Problem with Double Objectives
     Guo Dinghe, Zhang Kecun (Xi'an Jiaotong University, China)

An Exact Penalty Function for Multiobjective Programming
     (Haohai Long (Shanxi Economic Management Institute, China)

Controllability of Mechanical Systems with Differential Control Operator
     He Changzheng (Department of Applied Mathematics, Chengdu University of
     Science and Technology, China)

Mathematical Programming Used for Distributing Total Installed Capacity of
Hydro-Electric Plants
     Huang Qiang, Wang Shiding (Shaanxi Institute of Mechanical Engineering,
     China)

A Serial Optimization Method - Equiscalar Surface Strictest Constraint
Function Search Method 
     Huang Yongchang (The Computer Center of Dongfong Boiler Works, China)

Complementarily Problems of Set Functions and its Application in
Nondifferentiable Optimization
     Hu Xinsheng (Nanchang Teachers' College, China)

The Group Theoretic Approach and Decomposition for Integer Linear Programming
     Igor L. Averbakh (Chelyabinsk State Technical University, USSR)

Management of Optimization Models in Decision Support System
     Jingwen Li, Chun Yang (Second Artillery Engineering College, China)

Optimal Pricing of Delivery Priority and Spec. Levels for Semiconductor
Products
     Kyung Jo Min (Iowa State University, Iowa, U.S.A.)
     Shmuel S. Oren (University of California at Berkeley, Calif., U.S.A.)

Improving Methods of Linear Theory Method in Pipe Networks
     Linan Ni (Xi'an Institute of Metallurgy and Construction Engineering,
     China)

Parameter Optimization Method for Problems of Elastic Fluids
     Li Naicheng, Zhang Kecun (Xi'an Jiaotong University, China)

On the Corresponding Points of Contact, Line of Contact and Velocity Ratio of
Two Quadratic Arcs Which are Best Approximations to Involute Profiles
     Li Pingyuan, Pan Xiaoqin, Ding Deyong (Chongqing University, China)

On Best Approximations to Important Curves used in Mechanical Engineering by
Curves that are Easy to Produce
     Li Pingyuan, Gaong Chu, Yan Ahonghong, Zhao Xuejun, Zhen Jinhuan (Dept.
     of Appl. Math., Chongqing University, Chongqing, Sichuan, China)

Decomposition-Aggregation Method in Nonseparable Problems
     Litvinchev I.S. (Academy of Sciences of The USSR, USSR)

An Optimal Order Policy for Multi-Commodity Inventory System with Generalized
Reorder Cost
     Liu Baoding (Institute of Systems Science, Academia Sinica, China)

Optimal Conditions on the Quasidifferentiable Programming Subject to Ordinary-
type Constraints
     Liu Guangzhong (Chengdu University of Science and Technology, China)

Duality for Nonsmooth Pseudolinear Multiobjective Programming
     Liu Qinghui, Dong Jiaoli, Wang Liancheng (JiLin University of Technology,
     China)

Dualty in Nonsmooth Nonconvex Multiobjective Programming
     Liu Sanyang (Xidian University, China)

Cubic Potential for Strictly Nonlinear Oscillators 
     Li Yiping (Zhongshan University, China)

An Approach of Solving Extreme Value Problems with Equality Constraints
     Li Zemin (Chongqing Institute of Architecture and Engineering, China)

Linear Programming with AHP for Pollution Control of the Wei River
     Ma Guangwen, Wang Li (Shaanxi Institute of Mechanical Engineering, China)

Cone Duality Theorem of Semi-Infinite Programming Problem and Relative
Algorithm
     Ming Yue (People's Univ. of China, China)

A Simplifying Calculus on the Optimum Transport
     Nio Peiping (Lanzhou University, China)

Mathematical Modelling for Optimization of Uranium Mining
     Ou Feijun (Hengyang Institute of Technology, China)

The Application of Optimum Method in Wing Structure D-Design of Airplane
     Pen Benchen, Zhang Fan, Huang Shiqing (Computing Technique Research
     Institute, CAE, China)

The Numerical Method of Optimal Control for Parabolic Systems and its
Application to Some Inverse Problems of Thermal Bed Stimulation
     R.Kh. Yarulin, L.R. Mishne (Institute of Engergetics, USSR)

A 10-point Interpolatory Recursive Subdivision Algorithm for the Generation of
Parametric Surfaces
     Ruibin Qu (Brunel University, Britain)

Nonlinear Optimization Models for the New Spanish Autonomous Communities
Financing System
     Sergio Barba-Romero (Alcala University, Madrid, Spain)

A New Class of Collinear Scaling Algorithms for Unconstrained Optimization
     Sheng Songbai (Nanjing University, China)

Interval-Majorant Method for Global Optimization and its Applications
     Shen Zuhe (Nanjing University, China)

Two Classes of Superlinearly Convergent SQP-type Feasible Direction Methods
for Constrained Optimization
     Shi Baochang (Huazhong Univ. of Sci. & Tech., China)

Convergence Properties of Descent Methods Without Exact Line Searches
     Shiquan Wu (Institute of Applied Mathematics Academia Sinica, China)

Application of Minimized Matrix Norm Series to Structure Design
     Song Guoxiang, Duan Baoyan (Xidian University, China)

The Projection Reducing Dimensions Method for Interval Optimization
     Song Guoxiang (Xidian University, China)
     Shi Huli (Beijing Astronomical Observatory, China)

A General-purpose Parallel Algorithm for Unconstrained Optimization
     Stephen G. Nash, Ariela Sofer (Operations Research and Applied Statistics
     Dept., George Mason University, U.S.A.)

Goal Programming with Prefeerence Transform and an Interactive Algorithm 
     Sun Wei (Math. Section of Harbin Architecture and Civil Engineering
     Institute, China)

Quadratic Programming and Generalized Inverses
     Sun Wenyu (Nanjing University, China)

Stochastic Dynamic Programming and Optimal Dispatch of Hydro-Power Systems
     Sun Zhenxi, Dong Ziao (Beijing Economic Research Institute of Water
     Resources and Electric Power, China)

A New Algorithm for Optimal Streamflow Regulation of Cascade Hydro Reservior
Systems
     Tian Fengwei (Shaanxi Institute of Mechanical Engineering, China)

Convergence of Simplex Method for Two-variable Functions
     Zian Zhiyuan (Quingdao University, China)

An Application of Optimization Method - Fitting Several Parameters in
Pyrolysis Kinetic System of Equations
     Wang Daoyu, Xiao Xiumo (Technical College of the Armed Police Force,
     China)

A Global Sime-optimization Method for Multi-objectives
     Wang Dechao (Air Force Missile College)

On the Convergence of the Brent Method
     Wang Deren (Shanghai University of Science and Technology, China)
     Huang Zhijian (Fudan University, China)

A New Algorithm for Multi-objective Programming on the Optimal Design of Cam
Profile Curve
     Wang Huamin (Xi'an Jiaotong University, China)

Nonsmooth Multiobjective Programming
     Wang Liancheng, Dong Jiali (LiLin University of Technology, China)

Application of Linear Weighting Method of Multicriterion Group Decision Making
     Wang Shiding, Huang Qiang (Shaanxi Institute of Machanical Engineering)

A Quisi-Newton Method for a Kind of Nonlinear Programming with Linear
Constraints
     Wang Zhiwei, Jin Li (College of Engineering, University of Osaka
     Prefecture, Japan)

A Decomposition Algorithm and Its Parallelism for Block Linear Program Using
Affine Interior Method
     Wei Ziluan, Wu Li (Computing Center, Academia Sinica, China)

A New Algorithm for Unconstrained Minimax Optimization
     Wen Xiinhui (The Department of Industrial Manage Xinjiang Petroleum
     Institute, China)

Newton's Iteration Method and its Generalizations
     William J. Gilbert (University of Waterloo, Canada)

Integer Search Method for Integer Nonlinear Programming
     Wu Xingbao (Wuhan College of Metallurgic Marcagerial Codre, Wuhan Iron &
     Steel Complany, P.R. China)

A Direct Method and its Approximate Properties of Optimal Control Problem
     Wu Zheng, Zhang Guang Cheng (Chengdu University of Science and
     Technology, China)

Optimality Conditions and Duallty for a Class of Minimax Nondifferentiable
Fractional Programming Problems
     XiaoLin Wu, Kaizhou Chen (Xidian University, China)

Hierarchical Control Method for Multiobjective and Multimode System and its
Application
     Xie Jiancang, Yan Zhuqu (Shaanxi Institute of Mechanical Engineering,
     China)

Modelling of Flexible Robot Dynamics with Optimal Shape Functions
     Xu Chen (Xi'an Jiaotong University, China)
     Gan Xiaobing (Xidian University, China)

Parallel Methods for Optimization
     Xu Chengxian (Xi'an Jiaotong University, China)

A Class of Reduced Gradient Methods for Nonlinear Programming Problem with
Linear Constraints
     Xu Chengxian, Wei Bin (Xi'an Jiaotong University)

Dual Bundle Method for Nonsmooth Constrained Optimization
     Xu Huifu (Ningbo University, China)

Computation of Linear Programming and Nonlinear Programming
     Xu Jingjie (Daton Coal Mining Bureau, China)

On the Implementations of Interior-Point Methods
     Xu Xiaojie (Decision and Information System Institute of Systems Science,
     China)

Sign Matrix Regular Splittings and Monotonic Enclosures of Solutions for
Nonlinear System of Equations
     Xu Zongben (Institute for Computational and Applied Mathematics, Xi'an
     Jiaotong University, China)

K-T Sufficient Condition and Dual Theories of a Kind Function
     Yaguang Zhang, Chuanlong Wang (Shanxi Economic Management Institute,
     China)

The Software Package of Optimum Design for Valve Gear Mechanism of Internal
Combustion Engines
     Yang Boting, Zhang Kecun (Xi'an Jiaotong University, China)

Sufficient Optimality Conditions for Nonsmooth Multiobjective Programming
Problem
     Yang Xinmin (Chongqing Teacher's College, China)

Application of Boundary Fitted Coordinate in Porous Media Seepage Flow Compute
     Yan Junqi, Wu Peian, Zhao Yaodong (Northwest Hydrotechnic Research
     Institute, China)

Determination and Correction of an Inconsistent System of Linear Inequalities
     Yiyong Nie (Shenyang Institute of Computing Technology, Academia Sinica)

Duality and Optimality for Multistage Nonlinear Stochastic Programming with
Resource
     You Zhaoyong, Xu Chengxian, Chen Zhiping (Xi'an Jiaotong University,
     China)

The Mathematical Models of Environmental Planning for the Reservoir Region of
Hydropower Project
     Yurong Duan, Dan Yang (Dept. of Applied Mathematics, Congqing University,
     P.R.C.)
     Kangmin Liu (Dept. of Resources and Environmental Engineering, Chongping
     University, P.R.C.)

Numerical Methods for the Epidemic Model with Emigration of Population
     Zhai Qiliang (Nantong Teachers College, Jiangsu, China)
     Lu Guoping (Nantong Institute of Textile Engineering, China)

Optimization Application in Certain CAD Software System
     Zhang Changqi (Shaanxi Meth. and Elec. Institute, China)

Approximation Properties of Direct Method for Optimal Cdontrol Problems
     Zhang Guangcheng, Wu Zheng Guochuan (Chengdu University of Science and
     Technology, China)

Sufficient Conditions for Optimality of a Class of Semi-infinite Programming
in the Sense of (h, Phi)
     Zhang Qingxiang (Yanan University, China)

An Optimal Dicision Making in Selecting Teachers of Universities and
Insititute
     Zhang Weitao (The Northwestern Institute of Architectural Engineering,
     China)

The SQP Method for Signomial Geometric Programming
     Zhang Kecun (Xi'an Jiaotong University, China)
     Yang Boting (Xi'an Jiaotong University, China)

Consideration and Application on Cost Price of the Mathematical Programming
Model for Fresh Water Fishery
     Zheng Wenhai (Chongqing Teachers' College, China)

A Reduction Method in Integer Linear Programming
     Zhu Nan (Southwestern University of Finance and Economics, China)


-------------------------------------------------------------------------

   CHINESE JOURNAL OF ENGINEERING MATHEMATICS, Vol. 8 No. 2, June 1991

On Stability of Full Discrete Nonlinear Galerkin Method
     Li Kaitai (Institute for Computational & Applied Mathematics, Xi'an
     Jiaotong University)

A Hybrid Method for a Class of Semi-Infinite Programming
     Xu Chengxian, Chen Zhiping (Xi'an Jiaotong University)

Asymptotic Behavior of Almost-orbits of Asymptotically Nonexpansive Semigroups
in Banach Spaces
     Xu Hong-Kun (Institute of Applied Mathematics, East China University of
     Chemical Technology, Changhai 200237, China)

Region Analysis Approach for Constructing Solutions of Nonlinear Operator
Equations
     Xu Zongben (Xi'an Jiaotong University)
     M.A. Wolfe (University of St. Andrews)

Uniqueness Theorems for the Reduced Wave Equation with two Unbounded Media
     Zhang Bo (University of Strathclyde, Scotland; Xi'an Jiaotong University,
     P.R.C.)

Uniqueness of a-ASEC Codes for Length<8
     G. Fang
     H.C.A. van Tilborg (Eindhoven University of Technology, P.O. Box 513,
     5600 MB Eindhoven, the Netherlands)

On the Convexity of the Bernstein-Bezier Surfaces over Triangles
     Cheng Zhengxing (Xi'an Jiaotong University)

Lp-Inversion of the Diffusion Equation
     Liu Gui-Zhong (Eindhoven University of Technology, The Netherlands)

Robustness of Optimally Robust Controllers
     S.Q. Zhu (Department of Mathematics, Penn State University, Lehman, PA
     18627)

Unified Analysis of the Hybrid Form of Mixed Finite Elements for Second Order
Elliptic Problems
     Zhangxin Chen (Department of Mathematics, Purdue University, W.
     Lafayette, IN 47907, U.S.A.)

An Efficient Quadratic Approximation of Simple Singular Solutions
     Mei Zhen (Department of Mathematics, Xi'an Jiaotong University, Xi'an,
     Shaanxi Province, People's Republic of China)

Another Characterization of Hilbert Spaces
     Yao Lin (Yangzhou Teachers College)

Sequences in the Maximal Ideal Space of H  and Bourgain Algebra of Dougias
Algebra
     Sun Shunhua, Guo Kunyu (Sichan University)

The Orthoqonal Projects in Random Inner Product Spaces
     Lin Xi Ji mei Navigation Institute)
     Li Chuanmu (Xi'an Jiaotong University)

Multivariate Linear Statistical Relationship with Singular Covariance Matrix
     Dong Tianxin, Wu Kefa (Xi'an Jiaotong University)

The Bayesian Analysis of Vector Autoressive Processes
     Fan Chongjun (Xi'an Statistical College, Xi'an, China)
     Zhang Yaoting (Wuhan University, Wuhan, China)

The Shallow Water Equation and Its Numerical Simulation to a Lake Flow
     Fan Bijian (Xi'an Jiaotong University)

The Convergence of Solution to Burger's Equation with a Viscose Term
     Ma Yichen (Xi'an Jiaotong University)

Applying H-Matrices to Determining the Positive Stability of Matrices
     Yong Xuerong (Xi'an Jiaotong University)

Point Estimates for Simple Newton's Method
     Zhang Jiangshe (Xi'an Jiaotong University)

Regulazation Iterative Approximation for Solutions of Monotone Mapping
Equations
     Zhang Zhuosheng (Xi'an Jiaotong University)

Convegense of Two Iteative Methods for Undifferentiable Nonlinear Equations
     Pan Zhangyuan, Liu Xixing (Herbin Diangong Xueyuan)

Further Study of Steffensen-like Monotone Interation for Convex-Decomposable
Operator Equation
     Ling Yongxiang, Chen Baili (Xi'an Jiaotong University)

The Optimization Necessary Conditions to the Problems of Generalized
Inequality Constraints
     Yang Boting, Zhang Kecun (Xi'an Jiaotong University)

Convergence of 1-dimensional Discrete Newton Method
     Tian Zhiyuan (Qingdao University)

The System of Random Metric Spaces 
     Guo Tiexin (Xi'an Jiaotong University)
     Zhu Linhu (The Air Force Coll. of Engg.)

Ergodic Convergence for Asymptotically Nonexpansive Mappings in Uniformly
Convex Banach Space
     Xie Changyun (Northwest Textile Institute)

The Application of Optimal Method in Wing Structure Design of Airplane
     Pan Binchen, Zhang Fan, Huang Shiqin (Computing Technique Research
     Institute, CAE)

Local Proper Efficiency in Nondifferentiable Multiobjective Programming
     Liu Sanyang (Xidian University, Xi'an)

The Compatibility of a Variational Inequality
     Shen Jianzhong (Xi'an Jiaotong University)

----------------------------END OF REPORT--------------------------------

