International Series in Operations Research & Management Science
cover

Optimization Under Stochastic Uncertainty

Methods, Control and Random Search Methods

Authors: Marti, Kurt

  • 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
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イーブック ¥9,723
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  • イーブック版は、まもなく発売予定です。
  • 予定日: November 30, 2020
  • ISBN 978-3-030-55662-4
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ハードカバー ¥12,154
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • 予定日: November 30, 2020
  • ISBN 978-3-030-55661-7
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
  • Immediate ebook access, if available*, with your print order
この書籍について

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 of the probability distributions of the search variates (mutation random variables).


著者について

Kurt Marti is a Professor of Engineering Mathematics at the University of Bundeswehr Munich. He has been Chairman of the IFIP-Working Group 7.7 on “Stochastic Optimization” and  Chairman of the GAMM-Special Interest Group “Applied Stochastics and Optimization”. Professor Marti has published several books, both in German and in English and he is author of more than 160 papers in refereed journals and book chapters.

書籍の購入

イーブック ¥9,723
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • イーブック版は、まもなく発売予定です。
  • 予定日: November 30, 2020
  • ISBN 978-3-030-55662-4
  • ウォーターマーク付、 DRMフリー
  • ファイル形式:
  • どの電子書籍リーダーからでもすぐにお読みいただけます。
ハードカバー ¥12,154
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • 予定日: November 30, 2020
  • ISBN 978-3-030-55661-7
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
  • Immediate ebook access, if available*, with your print order
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書誌情報

Bibliographic Information
Book Title
Optimization Under Stochastic Uncertainty
Book Subtitle
Methods, Control and Random Search Methods
Authors
Series Title
International Series in Operations Research & Management Science
Series Volume
296
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
イーブック ISBN
978-3-030-55662-4
DOI
10.1007/978-3-030-55662-4
ハードカバー ISBN
978-3-030-55661-7
Series ISSN
0884-8289
Edition Number
1
Number of Pages
XIV, 387
Number of Illustrations
9 b/w illustrations
Topics

*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works and instructor copies are not included.