Optimization Under Stochastic Uncertainty - Methods, Control and Random Search Methods (Paperback, 1st ed. 2020)

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).

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	International Series in Operations Research & Management Science, 296
Release date:	November 2021
First published:	2020
Authors:	Kurt Marti
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	393
Edition:	1st ed. 2020
ISBN-13:	978-3-03-055664-8
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Computing & IT > General theory of computing > General Books > Computing & IT > Applications of computing > General Books > Business & Economics > Business & management > Management & management techniques > Operational research Promotions
LSN:	3-03-055664-6
Barcode:	9783030556648

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