Gradient-based simulation optimization under probability constraints

We study optimization problems subject to possible fatal failures. The probability of failure should not exceed a given confidence level. The distribution of the failure event is assumed unknown, but it can be generated via simulation or observation of historical data. Gradient-based simulation–opti...

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Bibliographic Details
Published in:European journal of operational research Vol. 212; no. 2; pp. 345 - 351
Main Authors: Andrieu, Laetitia, Cohen, Guy, Vázquez-Abad, Felisa J.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.07.2011
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Applied sciences
Computer simulation
Confidence intervals
Convergence
Decision theory. Utility theory
Estimation bias
Estimators
Exact sciences and technology
Failure
Mathematical analysis
Mathematics
Operational research and scientific management
Operational research. Management science
Optimization
Optimization algorithms
Optimization and Control
Parameter estimation
Portfolio theory
Probability constraints
Probability constraints Stochastic gradient algorithm Stochastic approximation
Probability distribution
Simulation
Solvers
Stochastic approximation
Stochastic gradient algorithm
Studies
Stochastic approximation
Probability constraints
Stochastic gradient algorithm
Gradient
Probabilistic approach
Bias
Finance
Rupture
Statistical simulation
Failures
Search algorithm
Confidence interval
Constrained optimization
Convolution
Convergence rate
Observation data
Reliability
Gradient method
Numerical convergence
Finite difference method
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:We study optimization problems subject to possible fatal failures. The probability of failure should not exceed a given confidence level. The distribution of the failure event is assumed unknown, but it can be generated via simulation or observation of historical data. Gradient-based simulation–optimization methods pose the difficulty of the estimation of the gradient of the probability constraint under no knowledge of the distribution. In this work we provide two single-path estimators with bias: a convolution method and a finite difference, and we provide a full analysis of convergence of the Arrow–Hurwicz algorithm, which we use as our solver for optimization. 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.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2011.01.049