Generalized Convexity and Vector Optimization (Nonconvex Optimization and Its Applications, 90),New

Product Description The present lecture note is dedicated to the study of the optimality conditions and the duality results for nonlinear vector optimization problems, in ?nite and in?nite dimensions. The problems include are nonlinear vector optimization problems, s metric dual problems, continuoustime 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 ?nance; 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 brie?y 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, Vinvex functions, and univex functions. Review 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 berzeugt durch seine gute und bersichtliche Form, seine konsequente detaillierter Behandlung vieler Problemklassen sowie den mathematischen Umfang der behandelten Probleme ...' (in: Rho Mathematik Verein der Uni Rostock, Mai 2009) From the Back Cover The present book discusses the KuhnTucker Optimality, KarushKuhnTucker Necessary and Sufficient Optimality Conditions in presence of various types of generalized convexity assumptions. Wolfetype Duality, MondWeir type Duality, Mixed type Duality for Multiobjective optimization problems such as Nonlinear programming problems, Fractional programming problems, Nonsmooth programming problems, Nondifferentiable programming problems, Variational and Control problems under various types of generalized convexity assumptions.