Convex Sets and Their Applications
Suitable for advanced undergraduates and graduate students, this text introduces the broad scope of convexity by highlighting diverse applications. Topics include characterizations of convex sets, polytopes, duality, optimization, and convex functions. Exercises appear throughout the text, with solutions, hints, and references at the end. 1982 edition.
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affine boundary point bounded Caratheodory’s Theorem closed convex set closed half-space compact convex set compact convex subset compact set constant width containing converse convex combination convex cone convex function convex hull convP convS Corollary Definition denote diameter disjoint dual cone equation Exercise exists a hyperplane exists a point extreme point fewer points Figure Find an example finite number ﬂat following theorem function f half-space Helly’s Theorem hyperplane H implies inequality interior intersection isoperimetric problem k-faces Lemma Let f let H line segment linear functional linear programming matrix game Maximize minimal n-dimensional nonempty compact convex nonempty compact subsets open set optimal solution optimal strategies perimeter polar set polygons polytope Prove the following radius real numbers relint Reuleaux triangle SECTION set of constant strictly separates subset of E subset of E2 subspace supporting hyperplane Suppose universal cover variables vector vertex vertices