Vector Variational Inequalities and Vect
โ Qamrul Hasan Ansari (auth.), Franco Giannessi (eds.)
๐ Library
๐
2000
๐ Springer US
๐ English
โฆ LIBER โฆ
๐
Vector Variational Inequalities and Vector Optimization: Theory and Applications
โ Scribed by Qamrul Hasan Ansari, Elisabeth Kรถbis, Jen-Chih Yao
- Publisher
- Springer International Publishing
- Year
- 2018
- Tongue
- English
- Leaves
- 517
- Series
- Vector Optimization
- Edition
- 1
- Category
- Library
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โฆ Synopsis
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.
โฆ Table of Contents
Front Matter ....Pages i-xiii
Preliminaries (Qamrul Hasan Ansari, Elisabeth Kรถbis, Jen-Chih Yao)....Pages 1-78
Analysis over Cones (Qamrul Hasan Ansari, Elisabeth Kรถbis, Jen-Chih Yao)....Pages 79-142
Solution Concepts in Vector Optimization (Qamrul Hasan Ansari, Elisabeth Kรถbis, Jen-Chih Yao)....Pages 143-180
Classical Methods in Vector Optimization (Qamrul Hasan Ansari, Elisabeth Kรถbis, Jen-Chih Yao)....Pages 181-222
Vector Variational Inequalities (Qamrul Hasan Ansari, Elisabeth Kรถbis, Jen-Chih Yao)....Pages 223-264
Linear Scalarization of Vector Variational Inequalities (Qamrul Hasan Ansari, Elisabeth Kรถbis, Jen-Chih Yao)....Pages 265-273
Nonsmooth Vector Variational Inequalities (Qamrul Hasan Ansari, Elisabeth Kรถbis, Jen-Chih Yao)....Pages 275-297
Generalized Vector Variational Inequalities (Qamrul Hasan Ansari, Elisabeth Kรถbis, Jen-Chih Yao)....Pages 299-338
Vector Equilibrium Problems (Qamrul Hasan Ansari, Elisabeth Kรถbis, Jen-Chih Yao)....Pages 339-427
Generalized Vector Equilibrium Problems (Qamrul Hasan Ansari, Elisabeth Kรถbis, Jen-Chih Yao)....Pages 429-485
Back Matter ....Pages 487-509
โฆ Subjects
Operation Research/Decision Theory
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