Simulation-Based Solution of Stochastic Mathematical Programs with Complementarity Constraints: Sample-Path Analysis

28 Pages Posted: 20 Mar 2004  

S. Ilker Birbil

Sabanci University - Graduate School of Management; Erasmus Research Institute of Management (ERIM)

Gül Gürkan

Tilburg University - Center for Economic Research (CentER)

Ovidiu Listes

affiliation not provided to SSRN

Date Written: 18 2004 2,

Abstract

We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated. Such programs can be used for modeling \average" or steady-state behavior of complex stochastic systems. Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models. Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints. The convergence analysis of sample-path methods rely heavily on stability conditions. We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence. Alongside we provide a complementary sensitivity result for the corresponding deterministic problems. In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions.

Keywords: stochastic mathematical programs with complementarity constraints, sample-path methods, simulation, stability, regularity conditions, mathematical programs with equilibrium constraints

JEL Classification: M, M11, R4, C62

Suggested Citation

Birbil, S. Ilker and Gürkan, Gül and Listes, Ovidiu, Simulation-Based Solution of Stochastic Mathematical Programs with Complementarity Constraints: Sample-Path Analysis (18 2004 2,). ERIM Report Series Reference No. ERS-2004-016-LIS. Available at SSRN: https://ssrn.com/abstract=513771

S. Ilker Birbil (Contact Author)

Sabanci University - Graduate School of Management ( email )

Istanbul, Orhanli, 34956 Tuzla
Turkey

Erasmus Research Institute of Management (ERIM) ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Gül Gürkan

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 2343 (Phone)
+31 13 466 3280 (Fax)

HOME PAGE: http://infolab.uvt.nl/people/ggurkan/

Ovidiu Listes

affiliation not provided to SSRN

No Address Available

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