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- W1569249351 abstract "In this work we study optimization problems subject to a failure constraint. This constraint is expressed in terms of a condition that causes failure, representing a physical or technical breakdown. We formulate the problem in terms of a probability constraint, where the level of confidence is a modelling parameter and has the interpretation that the probability of failure should not exceed that level. Application of the stochastic Arrow-Hurwicz algorithm poses two difficulties: one is structural and arises from the lack of convexity of the probability constraint, and the other is the estimation of the gradient of the probability constraint. We develop two gradient estimators with decreasing bias via a convolution method and a finite difference technique, respectively, and we provide a full analysis of convergence of the algorithms. Convergence results are used to tune the parameters of the numerical algorithms in order to achieve best convergence rates, and numerical results are included via an example of application in finance." @default.
- W1569249351 created "2016-06-24" @default.
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- W1569249351 date "2007-08-02" @default.
- W1569249351 modified "2023-09-23" @default.
- W1569249351 title "Stochastic Programming with Probability" @default.
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