Fundamentals of Convex Analysis: Duality, Separation, Representation, and Resolution

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.