Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2003-006 (May 23, 2003)

Smoothing Implicit Programming Approaches for Stochastic Mathematical Programs with Linear Complementarity Constraints
by Gui-Hua Lin, Xiaojun Chen and Masao Fukushima

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In this paper, we consider the stochastic mathematical program with equilibrium constraints (SMPEC), which can be thought as a generalization of the mathematical program with equilibrium constraints. Many decision problems can be formulated as SMPECs in practice. We discuss both lower-level wait-and-see and here-and-now decision problems. For the lower-level wait-and-see model, we propose a smoothing implicit programming method and establish a comprehensive convergence theory. For the here-and-now decision problem, we apply a penalty technique and suggest a similar method. We show that the two methods possess similar convergence properties.