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


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  • Ilker Birbil, S.
  • Gürkan, G.
  • Listes, O.L.

    (Tilburg University, Center for Economic Research)

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    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.

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    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2004-25.

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    Date of creation: 2004
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    Handle: RePEc:dgr:kubcen:200425

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    Keywords: stochastic processes; mathematics; stability; simulation; regulations; general equilibrium;

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    1. Still, G., 1999. "Generalized semi-infinite programming: Theory and methods," European Journal of Operational Research, Elsevier, vol. 119(2), pages 301-313, December.
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