Convexity and Optimization in Finite Dimensions I

Dantzig's development of linear programming into one of the most applicable optimization techniques has spread interest in the algebra of linear inequalities, the geometry of polyhedra, the topology of convex sets, and the analysis of convex functions. It is the goal of this volume to provide a synopsis of these topics, and thereby the theoretical background for the arithmetic of convex optimization to be treated in a subsequent volume. The exposition of each chapter is essentially independ...