Variational Analysis and Generalized Differentiation in Optimization and Control: In Honor of Boris S. Mordukhovich (Springer Optimization and Its Applications Book 47)

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. Front Matter....Pages i-x Systems of Vector Quasi-equilibrium Problems and Their Applications....Pages 1-42 Properties of Derivates and Some Applications....Pages 43-57 On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions....Pages 59-93 Future Challenges for Variational Analysis....Pages 95-107 A Deflected Subgradient Method Using a General Augmented Lagrangian Duality with Implications on Penalty Methods....Pages 109-132 On Weak Multifunction Equilibrium Problems....Pages 133-148 Optimality Conditions for a Simple Convex Bilevel Programming Problem....Pages 149-161 Smooth Representations of Optimal Solution Sets of Piecewise Linear Parametric Multiobjective Programs....Pages 163-176 Global Optimality Conditions for Classes of Non-convex Multi-objective Quadratic Optimization Problems....Pages 177-186 Application of Variational Analysis and Control Theory to Nonparametric Maximum Likelihood Estimation of a Density Function....Pages 187-203 Parametric Variational System with a Smooth-Boundary Constraint Set....Pages 205-221 Exact Penalty in Constrained Optimization and the Mordukhovich Basic Subdifferential....Pages 223-232 This book presents some 20 papers describing recent developments in advanced variational analysis, optimization, and control systems, especially those based on modern variational techniques and tools of generalized differentiation.