On the Existence of Solutions to Stochastic Mathematical Programs with Equilibrium Constraints

A. Evgrafov and M. Patriksson
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A. Evgrafov: Chalmers University of Technology
M. Patriksson: Chalmers University of Technology

Journal of Optimization Theory and Applications, 2004, vol. 121, issue 1, No 4, 65-76

Abstract: 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.

Keywords: Bilevel programming; equilibrium constraints; stochastic programming; existence of solutions; stochastic Stackelberg games; structural optimization (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTA.0000026131.04418.b7

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