Generalized Convexity and Vector Optimization / Edition 1

by Shashi K. Mishra, Shouyang Wang, Kin Keung Lai

Overview

The present lecture note is dedicated to the study of the optimality conditions and the duality results for nonlinear vector optimization problems, infinite and inflnite dimensions. The problems include are nonlinear vector optimization problems, s- metric dual problems, continuous-time vector optimization problems, relationships between vector optimization and variational inequality problems. Nonlinear vector optimization problems arise in several contexts such as in the building and interpretation of economic models; the study of various technolo- cal processes; the development of optimal choices in finance; management science; production processes; transportation problems and statistical decisions, etc. In preparing this lecture note a special effort has been made to obtain a se- contained treatment of the subjects; so we hope that this may be a suitable source for a beginner in this fast growing area of research, a semester graduate course in nonlinear programing, and a good reference book. This book may be useful to theoretical economists, engineers, and applied researchers involved in this area of active research. The lecture note is divided into eight chapters: Chapter 1 briefly deals with the notion of nonlinear programing problems with basic notations and preliminaries. Chapter 2 deals with various concepts of convex sets, convex functions, invex set, invex functions, quasiinvex functions, pseudoinvex functions, type I and generalized type I functions, V-invex functions, and univex functions.

Product Details

ISBN-13:	9783540856702
Publisher:	Springer Berlin Heidelberg
Publication date:	12/22/2008
Series:	Nonconvex Optimization and Its Applications , #90
Edition description:	2009
Pages:	294
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Generalized Convex Functions.- Generalized Type I and Related Functions.- Optimality Conditions.- Duality Theory.- Second and Higher Order Duality.- Symmetric Duality.- Vector Variational-like Inequality Problems.

Editorial Reviews

Aus den Rezensionen:

"… Das Buch ist eine sehr stringente und anspruchsvolle Aneinanderreihung von Definitionen, Lemmata, Theoremen und Korollaren sowie von deren Beweisen … Das vorliegende Werk ist … ein umfassendes und in seiner Tiefe beeindruckendes Fachbuch, es richtet sich … an Spezialisten auf dem Gebiet der Optimierung … Das Buch überzeugt durch seine gute und übersichtliche Form, seine konsequente detaillierter Behandlung vieler Problemklassen sowie den mathematischen Umfang der behandelten Probleme ..." (in: Rho - Mathematik Verein der Uni Rosk, Mai 2009)

From the Publisher