Generalized Convexity and Vector Optimization

1. Auflage. Softcover version of original hardcover Auflage 2009
ISBN: 978-3-642-09930-4
Verlag: Springer

Buch, Englisch, Band 90, 294 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 464 g

Reihe: Nonconvex Optimization and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Mishra, Shashi K.

Lai, Kin Keung

Wang, Shouyang

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder

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.