Twelve self-contained papers written by distinguished mathematicians in variational analysis, optimization, and control
First comprehensive treatment of the subject in book form
Presents several important new results and interdisciplinary research
Intended for a broad audience of engineers, economists, graduate students, researchers, and applied mathematicians
- 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 theMordukhovich 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 MethodUsing a General Augmented Lagrangian Duality With Implications on Penalty Methods.- 6. Adela Cap?t?, Gábor Kassay and Boglárka Mosoni, On Weak MultifunctionsEquilibrium Problems.- 7. S. Dempe, N. Dinh and J. Dutta, Optimality Conditions for a SimpleConvex Bilevel Programming Problem.- 8. Ya Ping Fang and Xiao Qi Yang, Smooth Representations of OptimalSolution Sets of Piecewise Linear Parametric Multiobjective Programs.- 9. V. Jeyakumar, G. M. Lee and G. Li, Global Optimality Conditions forClasses of Nonconvex Multi-objective Quadratic Optimization Problems.- 10. Ilya Shvartsman, Applications of Variational Analysis and Control Theoryto Non-Parametric Maximum Likelihood Estimation of a Density Function.- 11. J. C. Yao and N. D. Yen, Parametric Variational System With ASmooth-boundary Constraint Set.- 12. Alexander J. Zaslavski, Exact Penalty in Constrained Optimization andthe Mordukhovich Basic Subdifferential.
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.
Systems of Vector Quasi-equilibrium Problems and Their Applications.- Properties of Derivates and Some Applications.- On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions.- Future Challenges for Variational Analysis.- A Deflected Subgradient Method Using a General Augmented Lagrangian Dualitywith Implications on Penalty Methods.- On Weak Multifunction Equilibrium Problems.- Optimality Conditions for a Simple Convex Bilevel Programming Problem.- Smooth Representations of Optimal Solution Sets of Piecewise LinearParametric Multiobjective Programs.- Global Optimality Conditions for Classes of Non-convex Multi-objective Quadratic Optimization Problems.- Application of Variational Analysis and Control Theory to Nonparametric MaximumLikelihood Estimation of a Density Function.- Parametric Variational System with a Smooth-Boundary Constraint Set.- Exact Penalty in Constrained Optimization and the Mordukhovich BasicSubdifferential.
Inhaltsverzeichnis
- 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.
Klappentext
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 deillegalscription 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.
Twelve self-contained papers written by distinguished mathematicians in variational analysis, optimization, and control
First comprehensive treatment of the subject in book form
Presents several important new results and interdisciplinary research
Intended for a broad audience of engineers, economists, graduate students, researchers, and applied mathematicians
Includes supplementary material: sn.pub/extras
