<p>This volume summarizes and synthesizes an aspect of research work that has been done in the area of Generalized Convexity over the past few decades. Specifically, the book focuses on V-invex functions in vector optimization that have grown out of the work of Jeyakumar and Mond in the 1990’s. The authors integrate related research into the book and demonstrate the wide context from which the area has grown and continues to grow.</p>

V-Invex Functions and Vector Optimization (Springer Optimization and Its Applications, 14)

Business & Money

Wang, Shouyang

Mishra, Shashi K.

Lai, Kin-Keung

Management & Leadership

Springer

This volume summarizes and synthesizes an aspect of research work that has been done in the area of Generalized Convexity over the past few decades. Specifically, the book focuses on V-invex functions in vector optimization that have grown out of the work of Jeyakumar and Mond in the 1990’s. The authors integrate related research into the book and demonstrate the wide context from which the area has grown and continues to grow.

Invexity and Optimization presents results on invex function and their properties in smooth and nonsmooth cases, pseudolinearity and eta-pseudolinearity. Results on optimality and duality for a nonlinear scalar programming problem are presented, second and higher order duality results are given for a nonlinear scalar programming problem, and saddle point results are also presented. Invexity in multiobjective programming problems and Kuhn-Tucker optimality conditions are given for a multiobjecive programming problem, Wolfe and Mond-Weir type dual models are given for a multiobjective programming problem and usual duality results are presented in presence of invex functions. Continuous-time multiobjective problems are also discussed. Quadratic and fractional programming problems are given for invex functions. Symmetric duality results are also given for scalar and vector cases.

Invexity and Optimization (Nonconvex Optimization and Its Applications, 88)

Science & Math

Giorgi, Giorgio

Mathematics

<p>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.</p>

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

See the best price to sell, buy, or rent books by Mishra, Shashi K.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Mishra, Shashi K.

See the best price to sell, buy, or rent books by Mishra, Shashi K.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

V-Invex Functions and Vector Optimization (Springer Optimization and Its Applications, 14)

V-Invex Functions and Vector Optimization (Springer Optimization and Its Applications, 14)

Invexity and Optimization (Nonconvex Optimization and Its Applications, 88)

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