Vector Optimization and Monotone Operators via Convex Duality

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.

Presents the first approach to the maximal monotonicity of the diagonal operators by means of representative functions Introduces a framework for vector duality via general scalarizations Investigates the structure of the closedness-type regularity conditions in scalar optimization, showing how one can derive them

Auteur
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).

Contenu
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.