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Fundamentals of Convex Analysis

Duality, Separation, Representation, and Resolution

  • Book
  • © 1993

Overview

Authors:
  1. Michael J. Panik

    1. Department of Economics, University of Hartford, West Hartford, USA

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Preliminary Mathematics

    • Michael J. Panik
    Pages 1-33

  3. Convex Sets in Rn

    • Michael J. Panik
    Pages 35-48

  4. Separation and Support Theorems

    • Michael J. Panik
    Pages 49-75

  5. Convex Cones in Rn

    • Michael J. Panik
    Pages 77-120

  6. Existence Theorems for Linear Systems

    • Michael J. Panik
    Pages 121-132

  7. Theorems of the Alternative for Linear Systems

    • Michael J. Panik
    Pages 133-164

  8. Basic Solutions and Complementary Slackness in Pairs of Dual Systems

    • Michael J. Panik
    Pages 165-188

  9. Extreme Points and Directions for Convex Sets

    • Michael J. Panik
    Pages 189-234

  10. Simplicial Topology and Fixed Point Theorems

    • Michael J. Panik
    Pages 235-279

  11. Back Matter

    Pages 281-296
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Economics, University of Hartford, West Hartford, USA

    Michael J. Panik

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