Vector Optimization and Monotone Operators via Convex Duality: Recent Advances

by Sorin-Mihai Grad

Overview

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.

Product Details

ISBN-13:	9783319361901
Publisher:	Springer International Publishing
Publication date:	09/18/2015
Series:	Vector Optimization
Edition description:	Softcover reprint of the original 1st ed. 2015
Pages:	269
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

About the Author

Sorin-Mihai Grad is currently working within the Faculty of Mathematics of Chemnitz University of Technology, Germany, where he achieved his PhD in 2006 and his Habilitation in 2014. He is co-author of the book "Duality in Vector Optimization" (Springer, 2009).

Table of Contents

Introduction and preliminaries.- Duality for scalar optimization problems.- Minimality concepts for sets.- Vector duality via scalarization for vector optimization problems.- General Wolfe and Mond-Weir duality.- Vector duality for linear and semidefinite vector optimization problems.- Monotone operators approached via convex Analysis.