On the epiconvergence of stochastic optimization problems. (English) Zbl 1074.90552

Zervos, Mihail

Math. Oper. Res. 24, No. 2, 495-508 (1999).

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