Panik Fundamentals of Convex Analysis

Duality, Separation, Representation, and Resolution
1993
ISBN: 978-94-015-8124-0
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 24, 296 Seiten, eBook

Reihe: Theory and Decision Library B

offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called . In particular, it explores the topics of , , , and . 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. 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.

Zielgruppe

Research

Autoren/Hrsg.

Panik, M.J.

Inhaltsverzeichnis

0. Preface. 1. Preliminary Mathematics. 2. Convex Sets in R n . 3. Separation and Support Theorems. 4. Convex Cones in R n . 5. Existence Theorems for Linear Systems. 6. Theorems of the Alternative for Linear Systems. 7. Basic Solutions and Complementary Slackness in Pairs of Dual Systems. 8. Extreme Points and Directions for Convex Sets. 9. Simplicial Topology and Fixed Point Theorems. References. Notation Index. Index.