Variational Analysis and Generalized Differentiation in Optimization and Control

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.

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

Zusammenfassung

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.

Inhalt
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.