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Solving stochastic structural optimization problems by RSM-based stochastic approximation methods — gradient estimation in case of intermediate variables

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  • Kurt Marti

Abstract

Reliability-based structural optimization methods use mostly the following basic design criteria: I) Minimum weight (volume or costs) and II) high strength of the structure. Since several parameters of the structure, e.g. material parameters, loads, manufacturing errors, are not given, fixed quantities, but random variables having a certain probability distribution P,stochastic optimization problems result from criteria (I), (II), which can be represented by $$\mathop {\min }\limits_{x \in D} F(x)withF(x):=Ef(\omega ,x).$$ Here,f=f(ω,x) is a function on ℛ r depending on a random element ω, “E” denotes the expectation operator andD is a given closed, convex subset of ℛ r . Stochastic approximation methods are considered for solving (1), where gradient estimators are obtained by means of the response surface methodology (RSM). Moreover, improvements of the RSM-gradient estimator by using “intermediate” or “intervening” variables are examined. Copyright Physica-Verlag 1997

Suggested Citation

  • Kurt Marti, 1997. "Solving stochastic structural optimization problems by RSM-based stochastic approximation methods — gradient estimation in case of intermediate variables," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(3), pages 409-434, October.
    • Handle: RePEc:spr:mathme:v:46:y:1997:i:3:p:409-434
    DOI: 10.1007/BF01194863
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    Cited by:

    1. J. O. Royset & E. Polak, 2004. "Implementable Algorithm for Stochastic Optimization Using Sample Average Approximations," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 157-184, July.
    2. Louis Anthony Cox, 2020. "Answerable and Unanswerable Questions in Risk Analysis with Open‐World Novelty," Risk Analysis, John Wiley & Sons, vol. 40(S1), pages 2144-2177, November.

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