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Fundamentals of Convex Analysis

Duality, Separation, Representation, and Resolution

  • Michael J. Panik

Part of the Theory and Decision Library book series (TDLB, volume 24)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Michael J. Panik
    Pages 1-33
  3. Michael J. Panik
    Pages 35-48
  4. Michael J. Panik
    Pages 49-75
  5. Michael J. Panik
    Pages 77-120
  6. Michael J. Panik
    Pages 121-132
  7. Michael J. Panik
    Pages 133-164
  8. Michael J. Panik
    Pages 189-234
  9. Michael J. Panik
    Pages 235-279
  10. Back Matter
    Pages 281-296

About this book

Introduction

Fundamentals of Convex Analysis offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called convex analysis. In particular, it explores the topics of duality, separation, representation, and resolution. The work is intended for students of economics, management science, engineering, and mathematics who need exposure to the mathematical foundations of matrix games, optimization, and general equilibrium analysis. It is written at the advanced undergraduate to beginning graduate level and the only formal preparation required is some familiarity with set operations and with linear algebra and matrix theory. Fundamentals of Convex Analysis is self-contained in that a brief review of the essentials of these tool areas is provided in Chapter 1. Chapter exercises are also provided.
Topics covered include: convex sets and their properties; separation and support theorems; theorems of the alternative; convex cones; dual homogeneous systems; basic solutions and complementary slackness; extreme points and directions; resolution and representation of polyhedra; simplicial topology; and fixed point theorems, among others. A strength of this work is how these topics are developed in a fully integrated fashion.

Keywords

Complementary Slackness Grad calculus duality economics equilibrium general equilibrium linear algebra mathematical analysis mathematics optimization sets

Authors and affiliations

  • Michael J. Panik
    • 1
  1. 1.Department of EconomicsUniversity of HartfordWest HartfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8124-0
  • Copyright Information Springer Science+Business Media B.V. 1993
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4271-2
  • Online ISBN 978-94-015-8124-0
  • Buy this book on publisher's site