The reader will come to know about the present status of the research in this hot area of research field
The reader does not have to consult various research papers from different journals
Will provide the reader the present state of knowledge on research done in this area so far
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, 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 ?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, V-invex functions, and univex functions.
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.
The present book discusses the Kuhn-Tucker Optimality, Karush-Kuhn-Tucker Necessary and Sufficient Optimality Conditions in presence of various types of generalized convexity assumptions. Wolfe-type Duality, Mond-Weir 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.
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 Rostock, Mai 2009)
This book discusses the Kuhn-Tucker Optimality, Karush-Kuhn-Tucker Necessary and Sufficient Optimality Conditions in presence of various types of generalized convexity assumptions. It details the present state of knowledge on research done in this area.
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 Rostock, Mai 2009)
Inhaltsverzeichnis
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.
Klappentext
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, 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 ?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, V-invex functions, and univex functions.
The reader will come to know about the present status of the research in this hot area of research field
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The reader does not have to consult various research papers from different journals
n
Will provide the reader the present state of knowledge on research done in this area so far
n
Includes supplementary material: sn.pub/extras
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