On the Existence of Solutions to Stochastic Mathematical Programs with Equilibrium Constraints |
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Authors: | Evgrafov A. Patriksson M. |
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Affiliation: | (1) Department of Mathematics, Chalmers University of Technology, Gothenburg, Sweden;(2) Department of Mathematics, Chalmers University of Technology, Gothenburg, Sweden |
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Abstract: | We generalize stochastic mathematical programs with equilibrium constraints (SMPEC) introduced by Patriksson and Wynter (Ref. 1) to allow for the inclusion of joint upper-level constraints and to change the continuity assumptions with respect to the uncertainty parameters assumed before by measurability assumptions. For this problem, we prove the existence of solutions. We discuss also algorithmic aspects of the problem, in particular the construction of an inexact penalty function for the SMPEC problem. We apply the theory to the problem of structural topology optimization. |
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Keywords: | Bilevel programming equilibrium constraints stochastic programming existence of solutions stochastic Stackelberg games structural optimization |
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