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Convex Sets and Their Applications

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ISBN-10: 0486458032

ISBN-13: 9780486458038

Edition: 2007

Authors: Steven R. Lay

List price: $14.95
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Suitable for advanced undergraduates and graduate students, this text introduces the broad scope of convexity bynbsp;highlightingnbsp;diverse applications. Topics include families and characterizations of 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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Book details

List price: $14.95
Copyright year: 2007
Publisher: Dover Publications, Incorporated
Publication date: 6/5/2007
Binding: Paperback
Pages: 256
Size: 5.75" wide x 8.50" long x 0.51" tall
Weight: 0.594
Language: English

Linear Algebra and Topology
Convex Sets
Hyperplanes and Linear Functionals
Separating Hyperplanes
Supporting Hyperplanes
Helly-Type Theorems
Helly's Theorem
Kirchberger's Theorem
Kirchberger-type Theorems
Separation by a Spherical Surface
Separation by a Cylinder
Separation by a Parallelotope
Special Topics in E[superscript 2]
Sets of Constant Width
Universal Covers
The Isoperimetric Problem
Families of Convex Sets
Parallel Bodies
The Blaschke Selection Theorem
The Existence of Extremal Sets
Characterizations of Convex Sets
Local Convexity
Local Support Properties
Nearest-Point Properties
The Faces of a Polytope
Special Types of Polytopes and Euler's Formula
Approximation by Polytopes
Polarity and Polytopes
Dual Cones
Finite Matrix Games
Linear Programming
The Simplex Method
Convex Functions
Basic Properties
Support and Distance Functions
Continuity and Differentiability
Solutions, Hints, and References for Exercises