Numerical Optimization

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Springer Science & Business Media, Apr 28, 2000 - Mathematics - 636 pages
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This is a book for people interested in solving optimization problems. Because of the wide (and growing) use of optimization in science, engineering, economics, and industry, it is essential for students and practitioners alike to develop an understanding of optimization algorithms. Knowledge of the capabilities and limitations of these algorithms leads to a better understanding of their impact on various applications, and points the way to future research on improving and extending optimization algorithms and software. Our goal in this book is to give a comprehensive description of the most powerful, state-of-the-art, techniques for solving continuous optimization problems. By presenting the motivating ideas for each algorithm, we try to stimulate the reader’s intuition and make the technical details easier to follow. Formal mathematical requirements are kept to a minimum. Because of our focus on continuous problems, we have omitted discussion of important optimization topics such as discrete and stochastic optimization.
 

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Contents

Contents
1
Line Search Methods
3
Calculating Derivatives
7
References
9
34
36
ConvergenceRateofSteepestDescent
47
Index
50
CoordinateDescentMethods
53
ForwardMode
185
PropertiesofSR1Updating
207
SuperlinearConvergenceofBFGS
214
Nonlinear LeastSquares Problems
251
NotesandReferences
273
The Simplex Method
361
222
436
Penalty Barrier and Augmented Lagrangian Methods 488
489

OutlineoftheAlgorithm
67
TwoDimensionalSubspaceMinimization
74
TheHardCase
82
Conjugate Gradient Methods
101
NotesandReferences
132
TheReverseMode
179
NotesandReferences
523
224
586
5
613
RelationshipwithConjugateGradientMethods 227
617
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