Stochastic mathematical programs with equilibrium constraints, modelling and sample average approximation
نویسندگان
چکیده
In this article, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate the structure of both – the lower level equilibrium solution and objective integrand. We show almost sure convergence of optimal values, optimal solutions (both local and global) and generalized Karush–Kuhn–Tucker points of the SAA program to their true counterparts. We also study uniform exponential convergence of the sample average approximations, and as a consequence derive estimates of the sample size required to solve the true problem with a given accuracy. Finally, we present some preliminary numerical test results.
منابع مشابه
Approximating Stationary Points of Stochastic Mathematical Programs with Equilibrium Constraints via Sample Averaging
We investigate sample average approximation of a general class of onestage stochastic mathematical programs with equilibrium constraints. By using graphical convergence of unbounded set-valued mappings, we demonstrate almost sure convergence of a sequence of stationary points of sample average approximation problems to their true counterparts as the sample size increases. In particular we show ...
متن کاملStochastic Mathematical Programs with Equilibrium Constraints, Modeling and Sample Average Approximation
In this paper, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate the structure of both – the lower level equilibrium solution and objective integrand. We show almost sure convergence of optimal values, optimal solutions (both local and global) and general...
متن کاملStability Analysis of Two-Stage Stochastic Mathematical Programs with Complementarity Constraints via NLP Regularization
This paper presents numerical approximation schemes for a two stage stochastic programming problem where the second stage problem has a general nonlinear complementarity constraint: first, the complementarity constraint is approximated by a parameterized system of inequalities with a wellknown regularization approach [44] in deterministic mathematical programs with equilibrium constraints; the ...
متن کاملStochastic Programming with Equilibrium Constraints
In this paper we discuss here-and-now type stochastic programs with equilibrium constraints. We give a general formulation of such problems and study their basic properties such as measurability and continuity of the corresponding integrand functions. We also discuss consistency and rates of convergence of sample average approximations of such stochastic problems.
متن کاملA stochastic model for operating room planning under uncertainty and equipment capacity constraints
In the present economic context, the operating theater is considered as a critical activity in health care management. This paper describes a model for operating room (OR) planning under constraint of a unique equipment. At first level we schedule elective surgeries under the uncertainty of using a unique equipment. At the second level we consider emergency surgeries, and at the third le...
متن کامل