Convex Analysis: Theory and Applications
About this Title
G. G. Magaril-Il’yaev, Central Research Institute of Complex Automation, Moscow, Russia and V. M. Tikhomirov, Moscow State University, Moscow, Russia. Translated by Dmitry Chibisov
Publication: Translations of Mathematical Monographs
Publication Year: 2003; Volume 222
ISBNs: 978-0-8218-3525-8 (print); 978-1-4704-4646-8 (online)
MathSciNet review: MR2013877
MSC: Primary 49-02; Secondary 26B25, 52-02, 90C25, 90C46
Convex analysis is a branch of mathematics that studies convex sets, convex functions, and convex extremal problems. It has surprisingly diverse and fruitful applications in mathematics, mathematical physics, technology, and economics.
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.
The book can be used for an advanced undergraduate or graduate-level course on convex analysis and its applications. It is also suitable for independent study of this extremely important area of mathematics.
Advanced undergraduates, graduate students and research mathematicians interested in convex analysis.
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