Finite Dimensional Convexity and Optimization

Monique Florenzano, Cuong Le Van (auth.)3540415165, 9783540415169

The primary aim of this book is to present notions of convex analysis which constitute the basic underlying structure of argumentation in economic theory and which are common to optimization problems encountered in many applications. The intended readers are graduate students, and specialists of mathematical programming whose research fields are applied mathematics and economics. The text consists of a systematic development in eight chapters, with guided exercises containing sometimes significant and useful additional results. The book is appropriate as a class text, or for self-study.

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Table of contents :
Front Matter….Pages i-xii
Convexity in ℝ n ….Pages 1-19
Separation and Polarity….Pages 21-36
Extremal Structure of Convex Sets….Pages 37-50
Linear Programming….Pages 51-71
Convex Functions….Pages 73-86
Differential Theory of Convex Functions….Pages 87-107
Convex Optimization With Convex Constraints….Pages 109-127
Non Convex Optimization….Pages 129-139
Back Matter….Pages 141-154