| Gerhard-Wilhelm Weber | |
| Liqun Qi | |
| David Gao | |
| David Gao | |
| Yuhong Dai | |
| Xinmin Yang | |
| Charles Pearce | |
| Alex Rubinov | |
| Liqun Qi | |
| Xiaoqi Yang | |
| Dinh The Luc and Siegfried Schaible |
|
| Siegfried Schaible |
In July, 2000, the working group on continuous optimization, EUROPT, was founded in Budapest. Being a EURO group, nevertheless, scientists from all over the world are warmly welcome to participate at our annual workshop in Rotterdam, the Netherlands, July 12-13, 2001! It is entitled
"Smooth and Nonsmooth Optimization - Theory and Applications"Two new members joined the ORB Committee. They are
Alejandro Jofre (ajofre@dim.uchile.cl)
Dinh The Luc (dtluc@univ-avignon.fr)
POP now has 223 members from 27 countries. The ORB Committee wishes to serve POP members effectively. We also hope that all POP members may support ORB.
Duality Principles in Nonconvex Systems:
Theory, Methods and Applications
by
David Yang Gao
Dept. of Mathematics, Virginia Polytechnic and State
University, Blacksburg, USA
NONCONVEX OPTIMIZATION AND ITS APPLICATIONS
Volume 39
Short description:
Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems.For more details and for table of contents see:With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis.
Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.
Book Reviewed by G.A. Maugin:
.$B)5.(Bhe present book, beautifully written by David Y. Gao and richly documented, present such a framework with the introduction of a wealth of fundamental notions and an illustration of these through many examples issued essentially from mechanics, although econometrics and nonlinear programming, and some fields of physics such as phase transitions certainly belong to the same chapter. The author, a mathematician, does his best to render an arid field as pleasant as possible while maintaining the required mathematical rigor. This is achieved thanks to the vast culture of the author who does not hesitate to quote many aphorisms of western and oriental origins at some critical points. \x85
\x85 all mathematically-inclined mechanicians will find in this book some highly interesting solid substance, whether in the foundations or in the many applications. Selected chapters may be recommended for a graduate course. Applied mathematicians will find in it some inspiration via the numerous examples. Finally, literary critics and apprentice philosophers will get to know more about human nature through the numerous quotations and aphorisms.Applied Mechanics Review, Vol. 53, no. 9, 2000, B96.
Nonsmooth/Nonconvex Mechanics:
Modeling, Analysis and Numerical Methods
A Volume dedicated to the memory of Professor P.D.
Panagiotopoulos
Edited by: D.Y. Gao, R.W. Ogden and G.E. Stavroulakis
Kluwer Academic Publishers,
Nonconvex Optimization and Its Applications Vol. 50
Hardbound, ISBN 0-7923-6786-3, February 2001, 516 pp.
Short description:
Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity.This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics.The mathematical topics discussed in this book include variational and hemivariational inequalities, duality, complementarity, variational principles, sensitivity analysis, eigenvalue and resonance problems, and minimax problems. Applications are considered in the following areas among others: nonsmooth statics and dynamics, stability of quasi-static evolution processes, friction problems, adhesive contact and debonding, inverse problems, pseudoelastic modeling of phase transitions, chaotic behavior in nonlinear beams, and nonholonomic mechanical systems.
For more details and for table of contents see:
http://www.wkap.nl/book.htm/0-7923-6786-3
http://www.math.vt.edu/people/gao/books.html
The 3rd International Conference on Numerical Optimization and Numerical Linear Algebra (ICNONLA), organized by Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC) of Chinese Academy of Sciences and LanZhou Railway University, was successfully held in Dunhuang, China from May 17-20, 2001. The conference was sponsored by Chinese Natural Science Foundation, Chinese Mathematical Society and Chinese Society of Industrial and Applied Mathematics. The chairman of the organizing committee is Prof. Ya-xiang Yuan from ICMSEC, whereas the chairman of the scientific committee is Prof. Xiang-sun Zhang, who is the executive vice president of Academy of Mathematics and Systems Sciences of Chinese Academy of Sciences.
The conference invited many distinguished scientists in Numerical Optimization and Numerical Linear Algebra, including Prof. Yinyu Ye from Univ of Iowa, USA, Prof. Masao Fukushima from Kyoto Univ, Japan, Prof. Liqun Qi from Hong Kong Poly Univ, Prof. Oleg Burdakov from Linkoeping Univ, Sweden, Prof. Jianzhong Zhang from Hong Kong City Univ, and Prof. L. Luksan from Czech Republic and Technical Univ of Liberec, et al. Altogether, there are 64 participants, 40 of which are from the mainland of China and 24 from outside the mainland of China.
During the four-day conference, participants had full
discussions with one another. One special feature of this
conference is that, there was no parallel sessions. As a
result, each participant was able to hear all the talks and
their discussions. The weather of these days in Dunhuang were
also beautiful; this made the conference tour to Mao-gao Cave
and Whistling Sands Hill etc. more exciting and unforgetable.
Some pictures took during the conference could be download
from the webpages
(1) http://lsec.cc.ac.cn/~yyx/conf01.html
,
(2) http://www.cs.cas.cz/~luksan/icnonla.html
,
(3)
http://zzz.t.u-tokyo.ac.jp/zhang/dunhuang/Dunhuang-Conf.htm
.
Finally, I note here that this conference is the first one endorsed by POP. The next ICNONLA will be held two years later, namely, 2003. The conference site is to be determined. We welcome your attentions and your suggestions about the choice of the conference site very much.
Mathematicians in Australia interested in Optimization have instituted the practice of holding a one-day meeting of talks each year devoted to this area. There have been three such meetings to date, held in Melbourne, Perth and most recently in Ballarat, following on from a joint meeting of the American and Australian Mathematical Societies in Melbourne. These meetings have proved very successful and have also attracted participants from overseas.
This year Optimization Day will be held on 27 September,
2001, in McLaren Vale, just out of Adelaide, South Australia.
It is hoped that many of our friends from earlier
Optimization Days will be able to participate. We encourage
those interested in Optimization who have not been at an
Australian Optimization Day meeting before to come and meet
up with colleagues here. In the past there has been a special
volume published by Kluwer containing refereed versions of
talks presented at Optimization
Day. We plan a special volume this year also.
There will be a registration fee of $AU 100 which includes lunch, morning and afternoon teas on September 27 as well as a hard cover volume of published papers. For further information please email
OPTIMIZATIONDAY2001@maths.adelaide.edu.au
Optimization Day will be held at McLarens on the Lake, a
resort and conference centre in McLaren Vale, just out of
Adelaide. McLaren Vale is one of South Australia's premier
wine producing districts and is renowned for its natural
beauty and facilities
for gracious holiday living. It is close to beaches, the
Aldinga Aquatic Reserve, Port Noarlunga Reef and Onkaparinga
Gorge. There is a nearby golf course for relaxation. Overseas
visitors will find it an excellent starting point if they
wish to make an extended visit to the state.
A related event planned is ASOR2001, the 16th National
Conference of the Australian Society for Operations Research,
which is back to back with Optimization Day and held at the
same venue. For further information on this, please email
mailto:ASOR2001@maths.adelaide.edu.au
ASOR2001@maths.adelaide.edu.au
Important Dates
| 1 August 2001 | Deadline for Submission of Titles and Short Abstracts for Optimization Day Presentations | |
| 23 August 2001 | Optimization Day Program Published on Website | |
| 24 - 26 September 2001 | ASOR Conference | |
| 27 September 2001 | Optimization Day |
Publications
Authors of papers presented at Optimization Day will have
the opportunity to submit formal versions for publication in
a refereed volume of appropriate standing as was done for the
Ballarat and Perth meetings. Further details, including a
closing date for submissions, will be announced on
Optimization Day.
Many problems of data classifications (both supervised and unsupervised) can be reduced to unconstrained minimization of saw-tooth functions, which are expressed as the sum of a large number (some hundreds and even thousands) of fairly simple terms. These functions have very many shallow local minimizers, which are very close each to other. Some methods for local and global optimization, which were developed at University of Ballarat (Australia) for the last years, are suitable for minimising saw-tooth functions.
Combinations of a local search and a global search are the most profitable. However for the local search methods to be viable, only those methods which allow one to jump over many shallow local minima are good. In particular, derivative-free Discrete Gradient Method (DGM) (A. Bagirov, Derivative free methods for unconstrained nonsmooth optimization and its numerical analysis, Investigasao Operacional, vol 19, 75-93) enjoys this property. There are two versions of this method, one of them is based on Clarke subdifferential, and the other is based on the quasidifferential, introduced by V.F. Demyanov and A.M. Rubinov in 1980. It is appeared that the latter significantly outperform the former for saw-tooth functions. The Cutting Angle Method (CAM) (see for example, A. Rubinov, Abstract Convexity and Global Optimization, Kluwer Academic Publishers, 2000 and references therein) can be used for global optimization. This method allows one to leave a local minimizer fairly quickly.
The CAM is based on global optimization of some combinatorial problems. A. Bagirov and A. Rubinov suggested an analytic description of all local minimizers for these problems, which allows one to arrange sorting of local minimizers in order to find a global one. L. Batten and G. Beliakov from Deakin University (Melbourne) have recently developed a new version of this sorting; they suggest a fast algorithm for CAM, which is based on their approach.
The bundle CAM/DGM has demonstrated good results in applications to some real-world databases of small to medium size. First, it can be applied for unsupervised classification (to find clusters of a given finite set of points). Second, it can be applied to supervised classification, where there are at least two populations, which have been sampled. However, the current version of this bundle is not available for classification of large databases (where the product of number of records by the number of fields greater than 100.000). So the further development of both CAM and DGM is necessary. Results of numerical experiments confirm that the bundle CAM/DGM can be also applied for global minimization of various types of functions (not necessarily saw-tooth functions).
The 5th International Conference on Optimization: Techniques and Applications (ICOTA 2001) will be held in Hong Kong during December 15-17, 2001. It will be jointly organized by the Chinese University of Hong Kong, the City University of Hong Kong, and the Hong Kong Polytechnic University. It is a continuation of the ICOTA series, which has had its first four conferences in Singapore (1989 and 1992), Chendu, China (1995) and Perth, Australia (1998). Professor Xiaoqiang Cai in the Chinese University of Hong Kong, and I are the General Conference Co-Chairs of ICOTA 2001.
ICOTA 2001 has eight plenary speakers. They are:
Shu-Cherng Fang (USA)ICOTA 2001 will have three awards: ICOTA Theory Paper Award, ICOTA Application Paper Award, and ICOTA Student Paper Award. All the ICOTA 2001 nonplenary papers are eligible for the first two awards. ICOTA 2001 papers whose authors are all students or new graduates are eligible for the third award. The first two awards will be selected by
Masao Fukushima (Japan)
Toshihide Ibaraki (Japan)
David Luenberger (USA)
Angelo Miele (USA)
Panos Pardalos (USA)
Terry Rockafellar (USA)
Yinyu Ye (USA)
A) ICOTA Theory and Application Paper Award Committee:
Chair: Kok Lay Teo
Members: Toshihide Ibaraki
Duan Li (Secretary)
David Luenberger
Angelo Miele
Terry Rockafellar
Yinye Ye
The third award will be selected by
B) ICOTA Student Paper Award Committee:
Chair: Jiangzhong Zhang
Member: Shu-Cherng Fang
Masao Fukushima
Panos Pardalos
Xiaoqi Yang (Secretary)
After the Conference, a 3 day 2 night self paid conference cruiser tour to the Hainan Island will be organized.
The first announcement of ICOTA 2001 can be found on
http://www.se.cuhk.edu.hk/~icota
The second announcement of ICOTA 2001 will come soon.
This proceedings collects the copies of the documents used by the 32 invited speakers in their presentations during the International Workshop on Optimization with High Technology Applications, held in Hong Kong during 23-25 October 2000. This collection aims to provide a useful reference for researchers and postgraduate students in the area of optimization and its high-technology applications.
For further purchase details, please click here.
On June 1 – 4, 2001 the International Conference on Optimization and Optimal Control (ICOOC) was held at National Cheng Kung University in Tainan, Taiwan. This was the first major international meeting in the area of optimization ever organized in Taiwan. Over sixty researchers from Asia, Europe and North America took part in this conference to report on their latest results and new trends of research in the field. ICOOC was one of the first conferences endorsed by the newly founded Pacific Optimization Research Activity Group (POP).
The scientific program of the conference was rich. It consisted of sixteen plenary lectures given in the mornings. In the afternoons these were followed by shorter lectures organized in up to three streams of parallel sessions. At high scientific level the contributed talks provided overviews and new results in many important areas of modern optimization and optimal control.
The plenary lectures were given by A.R.Conn (USA), B.Datta (USA), S.C.Fang (USA), W.Kuo (USA), H.C.Lai (ROC), D.T.Luc (France, Vietnam), D.Pallaschke (Germany), P.M.Pardalos (USA), L.Qi (Hong Kong/PRC, Australia), T.Rockafellar (USA), S.Schaible (USA), M.H.Shi (ROC), T.Tanaka (Japan), K.L.Teo (Hong Kong/PRC), P.Tseng (USA) and P.L.Yu (USA).
Several of the twenty-one parallel sessions were grouped in clusters of sessions. The following topics were covered in the parallel sessions: Nonlinear Programming (I-III), Fuzzy Optimization, Fuzzy Decision Making and Management (I-II), Set-Valued Analysis (I-II), Generalized Convexity and Generalized Monotonicity (I-V), Computational Optimization and Applications, Resource Allocation and Multi-Criteria Optimization, Scheduling and Supply Chains, Mini-Symposium on Optimal Control (I-III), Control Theory and Applications (I-II).
A characteristic feature of this conference was a spirit of collaboration, beginning with the staff and students of Cheng Kung University who diligently and effectively worked together for a smooth running of the conference. Also, many researchers from abroad had been invited to various Taiwanese universities prior to the beginning of the conference, so that they had the opportunity to acquaint themselves with research activities at Taiwanese institutions and could participate in joint research with Taiwanese colleagues on topics of common interest. Even a workshop was organized prior to ICOOC at National Changhua University of Education by Professor L.J.Lin. Further evidence of a spirit of collaboration was the fact that many papers presented at this conference have been jointly written by colleagues from different regions.
For many participants this was their first visit to Taiwan which the Portuguese, the first western foreigners, called ‘Ihla Formosa’, the Beautiful Island. Like many countries in the Far East after World War II, Taiwan was poor with no significant industrial base. But now, it has become one of the five emerging regions in Asia which have been enjoying fast development of their economies during the last three decades. By following the freeway from Taipei in the North to Kaohsiung in the South one can observe many high tech companies along the route and many cities with huge blocks of buildings. The territory is well planned. Green open spaces stretching out from high mountains on the East to the seashores on the West are separating urban districts. This gives a pleasant view especially when one flies over the island from Taipei to Kaohsiung.
The city of Tainan which hosted the conference is particularly interesting. It is the oldest city of Taiwan and was capital of the island from 1682 to 1887. Actually the modern history of the area began in 1620 with the arrival of the Dutch. To give foreign participants a rough idea of the history and tradition of the city, the organizers spared half a day for a tour around the city which included a visit to three major historical sites: Fort Providentia, Fort Zeelandia and the Eternal Castle. Strolling through the streets of Tainan, one sees many temples of varying sizes displaying a variety of artwork, archways, gates and other historical documents.
The conference ended in the afternoon of June 4. Most of the participants rushed to pack their luggage for the trip home, at the same time somehow wishing to stay a bit longer on Ihla Formosa which is well known for its hospitality. The banquet at the conference had given us an excellent introduction to traditional Taiwanese cuisine. Those who could afford the time participated in a one-day tour after the conference to special sights on the island. Several participants also went hiking in the impressive mountains to the East before or after the conference.
The success of this conference is, without any doubt, due to the excellent organizational work of the Taiwanese colleagues from various institutions under the leadership of Professor Soon-Yi Wu, Chair of the Department of Mathematics at National Cheng Kung University. He and the local organizing committee chair, Professor Ruey-Lin Sheu with the support of staff members and many mathematics students organized a conference of high scientific caliber which will be remembered well by those who were privileged to participate in it.
In the previous issue of ORB I introduced the Working Group on Generalized Convexity. I had already mentioned that WGGC decided to hold its first international symposium outside North America and Europe. Generalized Convexity 7 will be hosted by the Hanoi Institute of Mathematics in Hanoi/Vietnam on August 27-31, 2002. Professor P.H.Sach, Hanoi and Professor J.E.Martinez-Legaz, Barcelona (currently WGGC chair) will serve as Program Co-Chairs. Professor N.D.Cong, Hanoi and Professor D.T.Luc, Avignon and Hanoi are co-chairing the Organizing Committee.
Generalized Convexity 7, organized by WGGC, has been endorsed by POP (Pacific Optimization Research Activity Group). Recently all POP members received the First Announcement of the conference. Meanwhile the list of invited speakers has been finalized. I am pleased to announce their names: Professor J.Borwein, Burnaby/Canada, Professor R.E.Burkhard, Graz/Austria, Professor B.Mordukhovich, Detroit/USA and Professor H.Tuy, Hanoi/Vietnam.
Generalized Convexity 7 is the first in this series of international symposia since 1980 to take place in the Far East. To help the communication process with present and future researchers in generalized convexity/generalized monotonicity in the Asia-Pacific region, we have asked several scientists actively involved in this area of research to serve as contact persons for their region regarding Generalized Convexity 7. They all graciously agreed to serve in this capacity. In the following paragraph I am listing their names. They all are members of POP. For your convenience I am listing their e-mail addresses as well.
Professor Q.H.Ansari (India, qhansari@ridaonline.com), Professor G.Y.Chen (China, machengy@polyu.edu.hk), Professor D.S.Kim (Korea, dskim@dolphin.pknu.ac.kr), Professor I.V.Konnov (Russia, ikonnov@ksu.ru), Professor D.T.Luc (Vietnam, dtluc@univ-avignon.fr), Professor A.M.Rubinov (Australia, a.rubinov@ballarat.edu.au), Professor T.Tanaka (Japan, tamaki@mathweb.sc.niigata-u.ac.jp), Professor X.Q.Yang (Hong Kong, mayangxq@polyu.edu.hk), and Professor J.-C.Yao (Taiwan, yaojc@ibm7.math.nsysu.edu.tw).
We encourage anyone in the Asia-Pacific region to keep in touch with “his/her” contact person in the list above, especially if somehow he/she has missed receiving the First Announcement of Generalized Convexity 7. In it a preliminary registration form was included which is to be sent to the conference office at gcm7@thevinh.ncst.ac.vn (Professor N.D.Cong, Co-Chair of the Organizing Committee). As the preparation of the conference progresses, please check the conference webpage at http://203.162.7.82/ and the WGGC webpage at http://genconv.ec.unipi.it/ for further information.
The current issue of ORB also contains a report by Professor D.T.Luc and myself on the International Conference on Optimization and Optimal Control (ICOOC ‘2001) in Tainan, Taiwan in June this year. At this first major international meeting in optimization ever organized in Taiwan, a sizable cluster of sessions on generalized convexity and generalized monotonicity was part of the program. The WGGC cluster was organized by Professor J.-C.Yao at National Sun Yat-sen University, Kaohsiung/Taiwan and myself. It brought together in the Far East a good number of researchers from different parts of the world. After this successful event in Taiwan we are looking forward to seeing many of you in Hanoi next August.