Convex analysis: theory and applications

G. G. Magaril-Ilyaev, V. M. Tikhomirov0821835254, 9780821835258

This book is an introduction to convex analysis and some of its applications. It starts with basic theory, which is explained within the framework of finite-dimensional spaces. The only prerequisites are basic analysis and simple geometry. The second chapter presents some applications of convex analysis, including problems of linear programming, geometry, and approximation. Special attention is paid to applications of convex analysis to Kolmogorov-type inequalities for derivatives of functions in one variable. Chapter 3 collects some results on geometry and convex analysis in infinite-dimensional spaces. A comprehensive introduction written “for beginners” illustrates the fundamentals of convex analysis in finite-dimensional spaces.

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Table of contents :
Front cover……Page 1
Title……Page 2
Title page……Page 3
Date-line……Page 4
Contents……Page 5
Preface……Page 7
Introduction……Page 9
1. Basic definitions……Page 33
2. Duality in convex analysis……Page 47
3. Convex calculus……Page 56
4. Finite-dimensional convex geometry……Page 65
5. Convex extremal problems……Page 77
6. Supplement: Convex analysis in vector spaces……Page 87
7. Convex analysis of subspaces and cones and the theory of linear equations and inequalities……Page 95
8. Classical inequalities, problems of geometry and mechanics……Page 100
9. Kolmogorov-type inequalities for derivatives……Page 107
10. Convex analysis and extremal problems of approximation and recovery……Page 126
11. Basic theorems of convex analysis……Page 161
12. Supplementary topics of convex analysis……Page 165
13. Convex analysis and the theory of extremum……Page 171
Bibliography……Page 185
Index……Page 189
Back cover……Page 193