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Table of Contents: Read more

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：

Table of Contents: Read more

Abstract Convexity of Elements of a Complete Lattice

Abstract Convexity of Subsets of a Set

Abstract Convexity of Functions on a Set

Abstract Quasi-Convexity of Functions on a Set

Dualities Between Complete Lattices

Dualities Between Families of Subsets

Dualities Between Sets of Functions

Conjugations. (-Dualities and <$$$>-Dualities

Abstract Subdifferentials

Notes and Remarks

References

Indexes

Abstract Convexity of Elements of a Complete Lattice

Abstract Convexity of Subsets of a Set

Abstract Convexity of Functions on a Set

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