Recent Developments in Vector Optimization

✍ Scribed by Gabriele Eichfelder, Johannes Jahn (auth.), Qamrul Hasan Ansari, Jen-Chih Yao (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2012
• Tongue: English
• Leaves: 576
• Series: Vector Optimization 1
• Edition: 1
• Category: Library

✦ Synopsis

We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc. one often encounters such kind of problems. The most important and difficult part in such problems is the conflict between various objectives and goals. In these problems, one has to find the minimum(or maximum) for several objective functions. Such problems are called vector optimization problems (VOP),multi-criteria optimization problems or multi-objective optimization problems. This volume deals with several different topics / aspects of vector optimization theory ranging from the very beginning to the most recent one. It contains fourteen chapters written by different experts in the field of vector optimization.

✦ Table of Contents

Front Matter....Pages i-xxiv
Vector Optimization Problems and Their Solution Concepts....Pages 1-27
Gordan-Type Alternative Theorems and Vector Optimization Revisited....Pages 29-59
Duality in Vector Optimization with Infimum and Supremum....Pages 61-94
Variable Ordering Structures in Vector Optimization....Pages 95-126
Strong KKT, Second Order Conditions and Non-solid Cones in Vector Optimization....Pages 127-167
Optimality Conditions and Image Space Analysis for Vector Optimization Problems....Pages 169-220
Nonsmooth Invexities, Invariant Monotonicities and Nonsmooth Vector Variational-Like Inequalities with Applications to Vector Optimization....Pages 221-274
Optimality Conditions for Approximate Solutions of Convex Semi-Infinite Vector Optimization Problems....Pages 275-295
Linear Fractional and Convex Quadratic Vector Optimization Problems....Pages 297-328
Levitin–Polyak Type Well-Posedness in Constrained Optimization....Pages 329-365
Vector Variational Principles for Set-Valued Functions....Pages 367-415
The Fermat Rule and Lagrange Multiplier Rule for Various Efficient Solutions of Set-Valued Optimization Problems Expressed in Terms of Coderivatives....Pages 417-466
Extended Pareto Optimality in Multiobjective Problems....Pages 467-515
Vector Optimization and Cooperative Games....Pages 517-545
Back Matter....Pages 547-551

✦ Subjects

Operations Research/Decision Theory; Optimization; Operations Research, Management Science