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
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.