Variational Analysis and Generalized Differentiation in Optimization and Control

1. Front Matter

   Pages i-x

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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

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.

• Boris S. Mordukhovich
• Convex Optimization
• Convex Set
• Generalized Subdifferential
• Variational Analysis
• Vector Function
• calculus
• differential equation
• maximum
• optimization
• system

• 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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