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Variational Analysis and Generalized Differentiation in Optimization and Control

In Honor of Boris S. Mordukhovich

  • Book
  • © 2010

Overview

Editors:
  1. Regina S. Burachik

    1. School of Mathematics & Statistics, Division of Information Technology, University of South Australia, Mawson Lakes, Australia

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  2. Jen-Chih Yao

    1. , Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan R.O.C.

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    You can also search for this editor in PubMed   Google Scholar

  • 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

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 47)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Systems of Vector Quasi-equilibrium Problems and Their Applications

    • Qamrul Hasan Ansari, Jen-Chih Yao
    Pages 1-42

  3. Properties of Derivates and Some Applications

    • Michael McAsey, Libin Mou
    Pages 43-57

  4. On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions

    • Robert Baier, Elza Farkhi, Vera Roshchina
    Pages 59-93

  5. Future Challenges for Variational Analysis

    • Jonathan M. Borwein
    Pages 95-107

  6. A Deflected Subgradient Method Using a General Augmented Lagrangian Duality with Implications on Penalty Methods

    • Regina S. Burachik, C. Yalçın Kaya
    Pages 109-132

  7. On Weak Multifunction Equilibrium Problems

    • Adela Capătă, Gábor Kassay, Boglárka Mosoni
    Pages 133-148

  8. Optimality Conditions for a Simple Convex Bilevel Programming Problem

    • S. Dempe, N. Dinh, J. Dutta
    Pages 149-161

  9. Smooth Representations of Optimal Solution Sets of Piecewise Linear Parametric Multiobjective Programs

    • Ya Ping Fang, Xiao Qi Yang
    Pages 163-176

  10. Global Optimality Conditions for Classes of Non-convex Multi-objective Quadratic Optimization Problems

    • V. Jeyakumar, G. M. Lee, G. Li
    Pages 177-186

  11. Application of Variational Analysis and Control Theory to Nonparametric Maximum Likelihood Estimation of a Density Function

    • Ilya Shvartsman
    Pages 187-203

  12. Parametric Variational System with a Smooth-Boundary Constraint Set

    • J.-C. Yao, N. D. Yen
    Pages 205-221

  13. Exact Penalty in Constrained Optimization and the Mordukhovich Basic Subdifferential

    • Alexander J. Zaslavski
    Pages 223-232
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Keywords

About this book

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.

Editors and Affiliations

  • School of Mathematics & Statistics, Division of Information Technology, University of South Australia, Mawson Lakes, Australia

    Regina S. Burachik

  • , Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan R.O.C.

    Jen-Chih Yao

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