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Finite Dimensional Convexity and Optimization : Studies in Economic Theory - Monique Florenzano

Finite Dimensional Convexity and Optimization

Studies in Economic Theory

Hardcover Published: 13th March 2001
ISBN: 9783540415169
Number Of Pages: 154

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This book discusses convex analysis, the basic underlying structure of argumentation in economic theory. Convex analysis is also common to the optimization of problems encountered in many applications. The text is aimed at senior undergraduate students, graduate students, and specialists of mathematical programming who are undertaking research into applied mathematics and economics. The text consists of a systematic development in eight chapters, and contains exercises. The book is appropriate as a class text or for self-study.

Notation
Convexity in R[superscript n]p. 1
Basic conceptsp. 1
Topological properties of convex setsp. 8
Separation and Polarityp. 21
Separation of convex setsp. 21
Polars of convex sets and orthogonal subspacesp. 28
Application to Minkowski-Farkas' lemmap. 29
Extremal Structure of Convex Setsp. 37
Extreme points and faces of convex setsp. 37
Application to linear inequalities. Weyl's theoremp. 40
Extreme points and extremal subsets of a polyhedral convex setp. 45
Linear Programmingp. 51
Necessary and sufficient conditions of optimalityp. 52
The duality theorem of linear programmingp. 54
The simplex methodp. 60
Convex Functionsp. 73
Basic definitions and propertiesp. 73
Continuity theoremsp. 76
Continuity properties of collections of convex functionsp. 79
Differential Theory of Convex Functionsp. 87
The Hahn-Banach dominated extension theoremp. 88
Sublinear functionsp. 89
Support functionsp. 91
Directional derivativesp. 92
Subgradients and subdifferential of a convex functionp. 93
Differentiability of convex functionsp. 98
Differential continuity for convex functionsp. 100
Convex Optimization With Convex Constraintsp. 109
The minimum of a convex function f: R[superscript n] [approaches]Rp. 110
Kuhn-Tucker Conditionsp. 111
Value functionsp. 123
Non Convex Optimizationp. 129
Quasi-convex functionsp. 129
Minimization of quasi-convex functionsp. 134
Differentiable optimizationp. 137
Appendixp. 141
Bibliographyp. 147
Indexp. 151
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540415169
ISBN-10: 3540415165
Series: Studies in Economic Theory
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 154
Published: 13th March 2001
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 1.27
Weight (kg): 0.42