Simulation-based solution of stochastic mathematical programs with complementarity constraints: sample-path analyis
AbstractWe consider a class of stochastic mathematical programs withcomplementarity constraints, in which both the objective and theconstraints involve limit functions or expectations that need to beestimated or approximated. Such programs can be used for modeling"average" or steady-state behavior of complex stochasticsystems. Recently, simulation-based methods have been successfullyused for solving challenging stochastic optimization problems andequilibrium models. Here we broaden the applicability of so-calledthe sample-path method to include the solution of certain stochasticmathematical programs with equilibrium constraints. The convergenceanalysis of sample-path methods rely heavily on stabilityconditions. We first review necessary sensitivity results, thendescribe the method, and provide sufficient conditions for itsalmost-sure convergence. Alongside we provide a complementarysensitivity result for the corresponding deterministic problems. Inaddition, we also provide a unifying discussion on alternative set ofsufficient conditions, derive a complementary result regarding theanalysis of stochastic variational inequalities, and prove theequivalence of two different regularity conditions.
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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2004-03.
Date of creation: 09 Mar 2004
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simulation; mathematical programs with equilibrium constraints; stability; regularity conditions; sample-path methods; stochastic mathematical programs with complementarity constraints;
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