Synopses & Reviews
A comprehensive textbook on convex sets. Develops the fundamental theory of convex sets, and discusses recent advances in mathematical research. Illustrates several important polytopes, including the four-dimensional case, and develops the theory of dual cones from a new perspective. Also considers linear programming, game theory, and convex functions. Contains over 475 exercises of varying difficulty, many with answers, hints, and references.
Table of Contents
Fundamentals.
Hyperplanes.
Helly-Type Theorems.
Kirchberger-Type Theorems.
Special Topics in E2.
Families of Convex Sets.
Characterizations of Convex Sets.
Polytopes.
Duality.
Optimization.
Convex Functions.
Solutions, Hints, and References for Exercises.
Bibliography.
Index.