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Optimization under stochastic uncert...

Marti, Kurt.

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Optimization under stochastic uncertainty = methods, control and random search methods /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Optimization under stochastic uncertainty/ by Kurt Marti.
Reminder of title:	methods, control and random search methods /
Author:	Marti, Kurt.
Published:	Cham :Springer International Publishing : : 2020.,
Description:	xiv, 393 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Operations research. -
Online resource:	https://doi.org/10.1007/978-3-030-55662-4
ISBN:	9783030556624

Optimization under stochastic uncertainty = methods, control and random search methods /
Marti, Kurt.

Optimization under stochastic uncertaintymethods, control and random search methods /[electronic resource] :by Kurt Marti. - Cham :Springer International Publishing :2020. - xiv, 393 p. :ill., digital ;24 cm. - International series in operations research & management science,v.2960884-8289 ;. - International series in operations research & management science ;v.296..

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)

ISBN: 9783030556624

Standard No.: 10.1007/978-3-030-55662-4doiSubjects--Topical Terms:

547123
Operations research.

LC Class. No.: T57.65 / .M37 2020

Dewey Class. No.: 658.4034

Optimization under stochastic uncertainty = methods, control and random search methods /
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520 $a 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)
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