Optimization by Vector Space Methods

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John Wiley & Sons, Jan 23, 1997 - Technology & Engineering - 352 pages
Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.

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Contents

INTRODUCTION
1
The Main Principles
8
2
14
NORMED LINEAR SPACES
22
HILBERT SPACE
46
APPROXIMATION
55
Approximation and Fourier Series
62
LEASTSQUARES ESTIMATION
78
GEOMETRIC FORM OF THE HAHNBANACH
129
LINEAR OPERATORS AND ADJOINTS
143
ADJOINTS
150
Duality Relations for Convex Cones
157
OPTIMIZATION OF FUNCTIONALS
169
GLOBAL THEORY OF CONSTRAINED OPTIMIZATION
213
LOCAL THEORY OF CONSTRAINED OPTIMIZATION
239
5
253

8
97
DUAL SPACES
103
EXTENSION FORM OF THE HAHNBANACH
110
7
116
ITERATIVE METHODS OF OPTIMIZATION
271
METHODS FOR SOLVING CONSTRAINED
297
SYMBOL INDEX
321
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About the author (1997)

DAVID G. LUENBERGER is a professor in the School of Engineering at Stanford University. He has published four textbooks and over 70 technical papers. Professor Luenberger is a Fellow of the Institute of Electrical and Electronics Engineers and recipient of the 1990 Bode Lecture Award. His current research is mainly in investment science, economics, and planning.

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