LEADER 04581oam 2200481 450 001 9910427046303321 005 20210420132858.0 010 $a3-030-55662-X 024 7 $a10.1007/978-3-030-55662-4 035 $a(CKB)4100000011569133 035 $a(MiAaPQ)EBC6388677 035 $a(DE-He213)978-3-030-55662-4 035 $a(PPN)252507185 035 $a(EXLCZ)994100000011569133 100 $a20210420d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOptimization under stochastic uncertainty $emethods, control and random search methods /$fKurt Marti 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XIV, 393 p. 9 illus.) 225 1 $aInternational series in operations research & management science ;$vVolume 296 311 $a3-030-55661-1 327 $a1. Optimal Control under Stochastic Uncertainty -- 2. Stochastic Optimization of Regulators -- 3. Optimal Open-Loop Control of Dynamic Systems under Stochastic Uncertainty -- 4. Construction of feedback control by means of homotopy methods -- 5. Constructions of Limit State Functions -- 6. Random Search Procedures for Global Optimization -- 7. Controlled Random Search under Uncertainty -- 8. Controlled Random Search Procedures for Global Optimization -- 9. Mathematical Model of Random Search Methods and Elementary Properties -- 10. Special Random Search Methods -- 11. Accessibility Theorems -- 12. Convergence Theorems -- 13. Convergence of Stationary Random Search Methods for Positive Success Probability -- 14. Random Search Methods of convergence order U(n?") -- 15. Random Search Methods with a Linear Rate of Convergence -- 16. Success/Failure-driven Random Direction Procedures -- 17. Hybrid Methods -- 18. Solving optimization problems under stochastic uncertainty by Random Search Methods(RSM). 330 $aThis 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). . 410 0$aInternational series in operations research & management science ;$vVolume 296. 606 $aOperations research 606 $aStochastic processes 615 0$aOperations research. 615 0$aStochastic processes. 676 $a658.4034 700 $aMarti$b Kurt$0223988 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a9910427046303321 996 $aOptimization under stochastic uncertainty$92222510 997 $aUNINA