Convex Sets and Their Applications
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.
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affine applications basic boundary bounded called Chapter circle column combination compact convex set compact convex subset conclude cone consider consists containing continuous conv converse convex function convex hull convex set corresponding cover Definition denote diameter dimension disjoint distance dual equal equation example Exercise exists extreme point face feasible fewer points Figure Find finite flat function function defined given holds hyperplane hyperplane H implies inequality interior intersection least Lemma Let F line segment linear linear functional matrix game Maximize minimal nonempty compact obtain origin parallel perimeter plane polytope positive possible problem PROOF Prove Prove the following radius relint respectively result sides simplex simplex method space strategy strictly separates subset of E Suppose Theorem triangle variables vector vertex vertices width