Finite Dimensional Convexity and Optimization

By: P. Gourdel, Monique Florenzano, Cuong Le Van

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Hardcover | 13 March 2001

At a Glance

Hardcover
172 Pages

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23.5 x 15.88 x 1.27

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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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You Can Find This Book In

Non-Fiction Medicine Medicine in General Mathematics Applied Mathematics Economics Economic Theory & Philosophy Calculus & Mathematical Analysis Functional Analysis & Transforms Optimisation Linear Programming Business & Management

Operational Research Game Theory

Notation
Convexity in R[superscript n]	p. 1
Basic concepts	p. 1
Topological properties of convex sets	p. 8
Separation and Polarity	p. 21
Separation of convex sets	p. 21
Polars of convex sets and orthogonal subspaces	p. 28
Application to Minkowski-Farkas' lemma	p. 29
Extremal Structure of Convex Sets	p. 37
Extreme points and faces of convex sets	p. 37
Application to linear inequalities. Weyl's theorem	p. 40
Extreme points and extremal subsets of a polyhedral convex set	p. 45
Linear Programming	p. 51
Necessary and sufficient conditions of optimality	p. 52
The duality theorem of linear programming	p. 54
The simplex method	p. 60
Convex Functions	p. 73
Basic definitions and properties	p. 73
Continuity theorems	p. 76
Continuity properties of collections of convex functions	p. 79
Differential Theory of Convex Functions	p. 87
The Hahn-Banach dominated extension theorem	p. 88
Sublinear functions	p. 89
Support functions	p. 91
Directional derivatives	p. 92
Subgradients and subdifferential of a convex function	p. 93
Differentiability of convex functions	p. 98
Differential continuity for convex functions	p. 100
Convex Optimization With Convex Constraints	p. 109
The minimum of a convex function f: R[superscript n] [approaches]R	p. 110
Kuhn-Tucker Conditions	p. 111
Value functions	p. 123
Non Convex Optimization	p. 129
Quasi-convex functions	p. 129
Minimization of quasi-convex functions	p. 134
Differentiable optimization	p. 137
Appendix	p. 141
Bibliography	p. 147
Index	p. 151
Table of Contents provided by Blackwell. All Rights Reserved.

Finite Dimensional Convexity and Optimization

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Hardcover

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