The book provides a self-contained and systematic treatment of algebraic and topological properties of convex sets in the n-dimensional Euclidean space. It benefits advanced undergraduate and graduate students with various majors in mathematics, optimization, and operations research. It may be adapted as a primary book or an additional text for any course in convex geometry or convex analysis, aimed at non-geometers. It can be a source for independent study and a reference book for researchers in academia.
The second edition essentially extends and revises the original book. Every chapter is rewritten, with many new theorems, examples, problems, and bibliographical references included. It contains three new chapters and 100 additional problems with solutions.
Contents:
Prerequisites
The Affine Structure of ℝn
Convex Sets
Convex Hulls
Cones and Conic Hulls
Recession Directions
Closedness Conditions
Cone Polarity and Normal Directions
Bounds, Supports, and Asymptotes
Separation Properties
Extreme Structure of Convex Sets
Exposed Structure of Convex Sets
Polyhedra
Solutions to Problems
Readership: Undergraduate and graduate students in mathematics, optimization and operations research.
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