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.
Author(s): Qamrul Hasan Ansari, Jen-Chih Yao (auth.), Regina S. Burachik, Jen-Chih Yao (eds.)
Series: Springer Optimization and Its Applications 47
Edition: 1
Publisher: Springer-Verlag New York
Year: 2010
Language: English
Pages: 232
Tags: Calculus of Variations and Optimal Control, Optimization; Systems Theory, Control; Optimization; Analysis
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
