Duality in Vector Optimization

by Radu Ioan Bot, Sorin-Mihai Grad, Gert Wanka

Overview

This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones a chapter on scalar conjugate duality follows. Then investigations on vector duality based on scalar conjugacy are made. Weak, strong and converse duality statements are delivered and connections to classical results from the literature are emphasized. One chapter is exclusively consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes. The monograph is closed with extensive considerations concerning conjugate duality for set-valued optimization problems.

Product Details

ISBN-13:	9783642028854
Publisher:	Springer Berlin Heidelberg
Publication date:	08/18/2009
Series:	Vector Optimization
Edition description:	2009
Pages:	400
Product dimensions:	6.40(w) x 9.30(h) x 1.20(d)

Table of Contents

Preliminaries on convex analysis and vector optimization.- Conjugate duality in scalar optimization.- Conjugate vector duality via scalarization.- Conjugate duality for vector optimization problems with finite dimensional image spaces.- Wolfe and Mond-Weir duality concepts.- Duality for set-valued optimization problems based on vector conjugacy.

Editorial Reviews

From the reviews:

“This book is dedicated to duality in vector optimization and is largely based on the contribution of the authors to this field. The book is divided into 7 chapters; it also contains a list of symbols and notations, an index of terms and a bibliography with 210 titles. … We recommend this book to researchers in convex scalar and vector optimization.”­­­ (Constantin Zălinescu, Mathematical Reviews, Issue 2010 i)

From the Publisher