Vector Optimization and Monotone Operators via Convex Duality : Recent Advances (Vector Optimization)

Grad, Sorin-Mihai

Springer International Publishing AG（2016/08発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 269 p.
• 商品コード 9783319361901

Full Description

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.

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.