Variational Analysis and Generalized Differentiation in Optimization and Control: In Honor of Boris S. Mordukhovich

ISBN-13: 9781441904362 / Angielski / Twarda / 2010 / 232 str.

Regina S. Burachik; Jen-Chih Yao

Opis

This special volume is dedicated to Boris M. Mordukhovich, on the occasion of his 60th birthday, and aims to celebrate his fundamental contributionsto variational analysis, generalizeddifferentiationand their applications.A main exampleof these contributions is Boris' recent opus magnus "Variational Analysis and Generalized Differentiation"(vols. I and II) 2,3]. A detailed explanationand careful description of Boris' research and achievements can be found in 1]. Boris' active work and jovial attitude have constantly inspired researchers of several generations, with whom he has generously shared his knowledgeand ent- siasm, along with his well-known warmth and human touch. Variationalanalysis is a rapidlygrowing?eld within pure and applied mathem- ics, with numerous applications to optimization, control theory, economics, en- neering, and other disciplines. Each of the 12 chapters of this volume is a carefully reviewed paper in the ?eld of variational analysis and related topics. Many chapters of this volume were presented at the International Symposium on Variational Analysis and Optimization (ISVAO), held in the Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, from November 28 to November 30, 2008. The symposium was organized in honour of Boris' 60thbirthday.It broughttogetherBorisandotherresearchersto discusssta- of-the-art results in variational analysis and its applications, with emphasis on op- mization and control. We thank the organizers and participants of the symposium, who made the symposium a highly bene?cial and enjoyable event. We are also grateful to all the authors of this special volume, who have taken the opportunityto celebrate Boris' birthdayand his decadesof contributionsto the area.

Spis treści

- 1. Qamrul Hasan Ansari and Jen-Chih Yao, Systems of Vector Quasi- Equilibrium Problems and their Applications. - 2. Michael McAsey and Libin Mou, Properties of Derivates and Some Applications. - 3. Robert Baier, Elza Farkhi and Vera Roshchina, On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions. - 4. Jonathan M. Borwein, Future Chanllenges for Variational Analysis. - 5. Regina S. Burachik and C. Yalç?n Kaya, A Deflected Subgradient Method Using a General Augmented Lagrangian Duality With Implications on Penalty Methods. - 6. Adela Cap?t?, Gábor Kassay and Boglárka Mosoni, On Weak Multifunctions Equilibrium Problems. - 7. S. Dempe, N. Dinh and J. Dutta, Optimality Conditions for a Simple Convex Bilevel Programming Problem. - 8. Ya Ping Fang and Xiao Qi Yang, Smooth Representations of Optimal Solution Sets of Piecewise Linear Parametric Multiobjective Programs. - 9. V. Jeyakumar, G. M. Lee and G. Li, Global Optimality Conditions for Classes of Nonconvex Multi-objective Quadratic Optimization Problems. - 10. Ilya Shvartsman, Applications of Variational Analysis and Control Theory to Non-Parametric Maximum Likelihood Estimation of a Density Function. - 11. J. C. Yao and N. D. Yen, Parametric Variational System With A Smooth-boundary Constraint Set. - 12. Alexander J. Zaslavski, Exact Penalty in Constrained Optimization and the Mordukhovich Basic Subdifferential.

Blurb

Variational analysis is a rapidly growing field within pure and applied mathematics, with numerous applications to optimization, control theory, economics, engineering, and other disciplines. This volume brings together state-of-the-art results in variational analysis and its applications, with an emphasis on optimization and control. The included chapters, written by international experts in the field of variational analysis and related topics, are dedicated to Boris S. Mordukhovich, a renowned mathematician, and aim to celebrate his fundamental contributions to variational analysis, generalized differentiation and their applications. This volume is intended for mathematicians studying variational analysis as well as other researchers interested in applying the principles of variational analysis to their area of study.