Set-valued Optimization: An Introduction with Applications

✍ Scribed by Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2015
• Tongue: English
• Leaves: 781
• Series: Vector Optimization
• Edition: 1
• Category: Library

✦ Synopsis

Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality and applications in economics among other things.

✦ Table of Contents

Front Matter....Pages i-xxii
Introduction....Pages 1-10
Order Relations and Ordering Cones....Pages 11-76
Continuity and Differentiability....Pages 77-108
Tangent Cones and Tangent Sets....Pages 109-211
Nonconvex Separation Theorems....Pages 213-248
Hahn-Banach Type Theorems....Pages 249-273
Conjugates and Subdifferentials....Pages 275-306
Duality....Pages 307-348
Existence Results for Minimal Points....Pages 349-368
Ekeland Variational Principle....Pages 369-397
Derivatives and Epiderivatives of Set-Valued Maps....Pages 399-508
Optimality Conditions in Set-Valued Optimization....Pages 509-604
Sensitivity Analysis in Set-Valued Optimization and Vector Variational Inequalities....Pages 605-643
Numerical Methods for Solving Set-Valued Optimization Problems....Pages 645-661
Applications....Pages 663-725
Back Matter....Pages 727-765

✦ Subjects

Optimization; Operation Research/Decision Theory; Continuous Optimization; Operations Research, Management Science; Game Theory, Economics, Social and Behav. Sciences