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by Stefan Schäffler (Author)
About this book
This self-contained monograph presents a new stochastic approach to global optimization problems arising in a variety of disciplines including mathematics, operations research, engineering, and economics. The volume deals with constrained and unconstrained problems and puts a special emphasis on large scale problems. It also introduces a new unified concept for unconstrained, constrained, vector, and stochastic global optimization problems. All methods presented are illustrated by various examples. Practical numerical algorithms are given and analyzed in detail.
The topics presented include the randomized curve of steepest descent, the randomized curve of dominated points, the semi-implicit Euler method, the penalty approach, and active set strategies. The optimal decoding of block codes in digital communications is worked out as a case study and shows the potential and high practical relevance of this new approach.
Global Optimization: A Stochastic Approach is an elegant account of a refined theory, suitable for researchers and graduate students interested in global optimization and its applications.
Brief contents
1 Stochastic Approach to Global Optimization at a Glance 1
1.1 Random Search. 1
1.2 Adaptive Search 4
1.3 Markovian Algorithms. 5
1.4 Population Algorithms. 6
2 Unconstrained Local Optimization 7
2.1 The Curve of Steepest Descent 7
2.2 Numerical Analysis 16
3 Unconstrained Global Optimization 21
3.1 A Randomized Curve of Steepest Descent 21
3.2 Concepts of Numerical Analysis 34
3.3 A Semi-implicit Euler Method 36
3.4 An Euler Method with Gradient Approximations 52
4 Application: Optimal Decoding in Communications Engineering 57
4.1 Channel Coding 57
4.2 Decoding 59
5 Constrained Global Optimization. 75
5.1 Introduction 75
5.2 A Penalty Approach.. 82
5.3 Equality Constraints 87
5.4 General Case 98
6 Vector Optimization 105
6.1 Introduction 105
6.2 The Curve of Dominated Points 106
6.3 A Randomized Curve of Dominated Points 110
6.4 An Euler Method. 112
6.5 Constraints 116
Appendix A: A Short Course in Probability Theory 119
Appendix B: Pseudorandom Numbers 127
Appendix C:White Noise Disturbances 133
Index 145
Series: Springer Series in Operations Research and Financial Engineering
Pages: 148 pages
Publisher: Springer; 2013 edition (June 26, 2012)
Language: English
ISBN-10: 9781461439264
ISBN-13: 978-1461439264
PDF version
Springer__Global Optimization.pdf
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EPUB version
Springer__Global Optimization.epub
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