Vector Optimization and Monotone Operators via Convex Duality: Recent Advances

✍ Scribed by Sorin-Mihai Grad (auth.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 282
• Series: Vector Optimization
• Edition: 1
• Category: Library

✦ Synopsis

This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.

✦ Table of Contents

Front Matter....Pages i-xvii
Introduction and Preliminaries....Pages 1-11
Duality for Scalar Optimization Problems....Pages 13-38
Minimality Concepts for Sets....Pages 39-59
Vector Duality via Scalarization for Vector Optimization Problems....Pages 61-113
General Wolfe and Mond-Weir Duality....Pages 115-175
Vector Duality for Linear and Semidefinite Vector Optimization Problems....Pages 177-221
Monotone Operators Approached via Convex Analysis....Pages 223-256
Back Matter....Pages 257-269

✦ Subjects

Operation Research/Decision Theory; Optimization; Continuous Optimization