Convex sets and their applications

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Convex sets and their applications / Steven R. Lay

資料種別:: 図書
出版情報:: New York : Wiley, c1982
形態:: xvi, 244 p. ; 25 cm
シリーズ名:: Pure and applied mathematics : a Wiley-Interscience series of texts, monographs, and tracts <BA00007488>
著者名:: Lay, Steven R., 1944- <DA02272624>
ISBN:: 9780471095842 [0471095842]
書誌ID:: BA03785989

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注記:

"A Wiley-Interscience publication."
Bibliography: p. 234-238
Includes indexes

主題:

Convex sets

言語:

英語

目次情報:

Fundamentals / 1：

Linear Algebra and Topology

Convex Sets / 2：

Hyperplanes

Hyperplanes and Linear Functionals / 3：

Separating Hyperplanes / 4：

Supporting Hyperplanes / 5：

Helly-Type Theorems

Helly's Theorem / 6：

Kirchberger's Theorem / 7：

Kirchberger-type Theorems

Separation by a Spherical Surface / 8：

Separation by a Cylinder / 9：

Separation by a Parallelotope / 10：

Special Topics in E[superscript 2]

Sets of Constant Width / 11：

Universal Covers / 12：

The Isoperimetric Problem / 13：

Families of Convex Sets

Parallel Bodies / 14：

The Blaschke Selection Theorem / 15：

The Existence of Extremal Sets / 16：

Characterizations of Convex Sets

Local Convexity / 17：

Local Support Properties / 18：

Nearest-Point Properties / 19：

Polytopes

The Faces of a Polytope / 20：

Special Types of Polytopes and Euler's Formula / 21：

Approximation by Polytopes / 22：

Duality

Polarity and Polytopes / 23：

Dual Cones / 24：

Optimization

Finite Matrix Games / 25：

Linear Programming / 26：

The Simplex Method / 27：

Convex Functions

Basic Properties / 28：

Support and Distance Functions / 29：

Continuity and Differentiability / 30：

Solutions, Hints, and References for Exercises

Bibliography

Index

Fundamentals / 1：

Linear Algebra and Topology

Convex Sets / 2：

Hyperplanes

Hyperplanes and Linear Functionals / 3：

Separating Hyperplanes / 4：

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