Authors:
- Presents Stochastic Optimization/Control Methods and Random Search Methods (RSM) in one volume
- Presents Homotopy methods for solving control problems under stochastic uncertainty
- Includes convergence, convergence rates and convergence acceleration of Random Search Methods
- Presents studies of computation of optimal feedback controls by means of optimal open-feedback controls
- Provides construction methods for Limit State Functions for engineering structures or systems under stochastic uncertainty
Part of the book series: International Series in Operations Research & Management Science (ISOR, volume 296)
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Table of contents (18 chapters)
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Front Matter
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Stochastic Optimization Methods
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Front Matter
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Optimization by Stochastic Methods: Foundations and Optimal Control/Acceleration of Random Search Methods (RSM)
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Front Matter
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Random Search Methods (RSM): Convergence and Convergence Rates
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Front Matter
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About this book
This book examines application and methods to incorporating stochastic parameter variations into the optimization process to decrease expense in corrective measures. Basic types of deterministic substitute problems occurring mostly in practice involve i) minimization of the expected primary costs subject to expected recourse cost constraints (reliability constraints) and remaining deterministic constraints, e.g. box constraints, as well as ii) minimization of the expected total costs (costs of construction, design, recourse costs, etc.) subject to the remaining deterministic constraints.
After an introduction into the theory of dynamic control systems with random parameters, the major control laws are described, as open-loop control, closed-loop, feedback control and open-loop feedback control, used for iterative construction of feedback controls. For approximate solution of optimization and control problems with random parameters and involving expected cost/loss-type objective,constraint functions, Taylor expansion procedures, and Homotopy methods are considered, Examples and applications to stochastic optimization of regulators are given. Moreover, for reliability-based analysis and optimal design problems, corresponding optimization-based limit state functions are constructed. Because of the complexity of concrete optimization/control problems and their lack of the mathematical regularity as required of Mathematical Programming (MP) techniques, other optimization techniques, like random search methods (RSM) became increasingly important.Basic results on the convergence and convergence rates of random search methods are presented. Moreover, for the improvement of the – sometimes very low – convergence rate of RSM, search methods based on optimal stochastic decision processes are presented. In order to improve the convergence behavior of RSM, the random search procedure is embedded into a stochastic decision process for an optimal control ofthe probability distributions of the search variates (mutation random variables).
Keywords
Authors and Affiliations
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Institute for Mathematics and Computer Science, University of Bundeswehr Munich, Munich, Germany
Kurt Marti
About the author
Bibliographic Information
Book Title: Optimization Under Stochastic Uncertainty
Book Subtitle: Methods, Control and Random Search Methods
Authors: Kurt Marti
Series Title: International Series in Operations Research & Management Science
DOI: https://doi.org/10.1007/978-3-030-55662-4
Publisher: Springer Cham
eBook Packages: Business and Management, Business and Management (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-55661-7Published: 11 November 2020
Softcover ISBN: 978-3-030-55664-8Published: 11 November 2021
eBook ISBN: 978-3-030-55662-4Published: 10 November 2020
Series ISSN: 0884-8289
Series E-ISSN: 2214-7934
Edition Number: 1
Number of Pages: XIV, 393
Number of Illustrations: 9 b/w illustrations
Topics: Operations Research/Decision Theory, Probability Theory and Stochastic Processes, Computer Science, general