A course on optimization and best approximation Holmes, Richard B.

By:

Holmes, Richard B

Material type: Text

TextSeries: Lecture notes in mathematics; 257Publication details: Springer 1972 BerlinDescription: viii, 233 pISBN:

9783540057642

Subject(s):

DDC classification:

510.8 H6C6

Summary: This is a paperback book published by Spring-Verlag in 1972 as Volume 257 of Lecture Notes in Mathematics. Chapters include: Preliminaries; Theory of optimization; Theory of best approximation; Comments on the problems, and Selected special topics. There are numerous examples and equations. Holmes published this book while at Purdue University, Indiana.

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Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Book	Ahmedabad	Non-fiction	510.8 H6C6 (Browse shelf(Opens below))	Available		191917

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Table of Contents:

Part I. Preliminaries . . . . . . . . . . . . . . . . . . . .

Notation . . . . . . . . . . . . . . . . . . . . . . 1
The Hahn-Banach Theorem . . . . . . . . . . . . . 2
The Separation Theorems . . . . . . . . . . . . . . 4
The Alaoglu-Bourbaki Theorem . . . . . . . . . . . . 7
The Krein-Milman Theorem . . . . . . . . . . . . . . 8

Part II. Theory of Optimization . . . . . . . . . . . . . . .

Convex Functions . . . . . . . . . . . . . . . . . . 14
Directional Derivatives . . . . . . . . . . . . . . 16
Subgradients . . . . . . . . . . . . . . . . . . . . 20
Normal Cones . . . . . . . . . . . . . . . . . . . . 23
Subdifferential Formulas . . . . . . . . . . . . 25
Convex Programs . . . . . . . . . . . . . . . . . . 29
Kuhn-Tucker Theory . . . . . . . . . . . . . . . . . 32
Lagrange Multipliers . . . . . . . . . . . . . . . . 36
Conjugate Functions . . . . . . . . . . . . . . . . 42
Polarity . . . . . . . . . . . . . . . . . . . . . . 48
Dubovitskii-Milyutin Theory . . . . . . . . . . . . 51
An Application . . . . . . . . . . . . . . . . . . . 56
Conjugate Functions and Subdifferentials ...... 58
Distance Functions . . . . . . . . . . . . . . . . . 61
The Fenchel Duality Theorem . . . . . . . . . . . . 65
Some Applications .

Part III. Theory of Best Approximation • . . . . . . . . . .

Characterization of Best Approximations ...... 76
Extremal Representations . . . . . . . . . . . . . . 81
Application to Gaussian Quadrature . . . . . . . . . 88
Haar Subspaces . . . . . . . . . . . . . . . . . . . 91
Chebyshev Polynomials . . . . . . . . . . . . . . . 98
Rotundity . . . . . . . . . . . . . . . . . . . . . 105
Chebyshev Subspaces . . . . . . . . . . . . . . . . 109
Algorithms for Best Approximation . . . . . . . . . 118
Proximinal Sets . . . . . . . . . . . . . . . . . . 123
Theory of Optimization . . . . . . . . . . . . . . .
Convex Functions . . . . . . . . . . . . . . . . . . 14
Directional Derivatives . . . . . . . . . . . . . . 16
Subgradients . . . . . . . . . . . . . . . . . . . . 20
Normal Cones . . . . . . . . . . . . . . . . . . . . 23
Subdifferential Formulas . . . . . . . . . . . . 25
Convex Programs . . . . . . . . . . . . . . . . . . 29
Kuhn-Tucker Theory . . . . . . . . . . . . . . . . . 32
Lagrange Multipliers . . . . . . . . . . . . . . . . 36
Conjugate Functions . . . . . . . . . . . . . . . . 42
Polarity . . . . . . . . . . . . . . . . . . . . . . 48
Dubovitskii-Milyutin Theory . . . . . . . . . . . . 51
An Application . . . . . . . . . . . . . . . . . . . 56
Conjugate Functions and Subdifferentials ...... 58
Distance Functions . . . . . . . . . . . . . . . . . 61
The Fenchel Duality Theorem . . . . . . . . . . . . 65
Some Applications . . . . . . . . . . . . . . . . . 7O

Part IV. Comments on the Problems . . . . . . . . . . . . . . .

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Part V" Selected Special Topics s . . . . . . . . . . . . . . . .

E-spaces . . . . . . . . . . . . . . . . . . . . . . . 145
Metric Projections . . . . . . . . . . . . . . . . . . 157
Optimal Estimation . . . . . . . . . . . . . . . . . . 177
Quasi-Solutions . . . . . . . . . . . . . . . . . . . 203
Generalized Inverses . . . . . . . . . . . . . . . . . 214

This is a paperback book published by Spring-Verlag in 1972 as Volume 257 of Lecture Notes in Mathematics. Chapters include: Preliminaries; Theory of optimization; Theory of best approximation; Comments on the problems, and Selected special topics. There are numerous examples and equations. Holmes published this book while at Purdue University, Indiana.

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