Vector Variational Inequalities and Vector Optimization: Theory and Applications

Description

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization. Front Matter ....Pages i-xiii Preliminaries (Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao)....Pages 1-78 Analysis over Cones (Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao)....Pages 79-142 Solution Concepts in Vector Optimization (Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao)....Pages 143-180 Classical Methods in Vector Optimization (Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao)....Pages 181-222 Vector Variational Inequalities (Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao)....Pages 223-264 Linear Scalarization of Vector Variational Inequalities (Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao)....Pages 265-273 Nonsmooth Vector Variational Inequalities (Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao)....Pages 275-297 Generalized Vector Variational Inequalities (Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao)....Pages 299-338 Vector Equilibrium Problems (Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao)....Pages 339-427 Generalized Vector Equilibrium Problems (Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao)....Pages 429-485 Back Matter ....Pages 487-509