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On the epiconvergence of stochastic optimization problems. (English) Zbl 1074.90552
Summary: The problem of strong consistency of sequences of optimal solutions to stochastic optimization problems is considered. This problem is related to a large number of applications, including Bayesian decision problems and Monte Carlo simulations, as well as a number of statistical methodologies such as maximum likelihood estimation. The theory of epiconvergence being a framework within which such results can be established, the epiconvergence of the performance criteria of a sequence of stochastic optimization problems is proved under simple weak assumptions.

MSC:
90C15 Stochastic programming
49J45 Methods involving semicontinuity and convergence; relaxation
65C05 Monte Carlo methods
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