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Generalized Convexity and Vector Optimization

  • Book
  • © 2009

Overview

Authors:
  1. Shashi Kant Mishra

    1. Department of Mathematics, Banaras Hindu University, Varanasi, India

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  2. Shou-Yang Wang

    1. Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, People's Republic of China

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    You can also search for this author in PubMed   Google Scholar

  3. Kin Keung Lai

    1. Department of Management Sciences, City University of Hong Kong, Kowloon Tong, Hong Kong

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  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Nonconvex Optimization and Its Applications (NOIA, volume 90)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    Pages 1-5

  3. Generalized Convex Functions

    Pages 7-24

  4. Generalized Type I and Related Functions

    Pages 25-43

  5. Optimality Conditions

    Pages 45-90

  6. Duality Theory

    Pages 91-164

  7. Second and Higher Order Duality

    Pages 165-197

  8. Symmetric Duality

    Pages 199-253

  9. Vector Variational-like Inequality Problems

    Pages 255-279

  10. Back Matter

    Pages 281-294
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Banaras Hindu University, Varanasi, India

    Shashi Kant Mishra

  • Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, People's Republic of China

    Shou-Yang Wang

  • Department of Management Sciences, City University of Hong Kong, Kowloon Tong, Hong Kong

    Kin Keung Lai

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