Department of Applied Mathematics & Physics, Kyoto University
Technical Report 2005-003 (May 17, 2005)
Solving Stochastic Mathematical Programs with Equilibrium Constraints via Approximation and Smoothing Implicit Programming with Penalization
by Gui-Hua Lin, Xiaojun Chen and Masao Fukushima
In this paper, we consider the
stochastic mathematical programs with equilibrium constraints,
which includes two kinds of models called here-and-now and
lower-level wait-and-see problems. We present a combined smoothing
implicit programming and penalty method for the problems with a
finite sample space. Then, we suggest a quasi-Monte Carlo
approximation method for solving a problem with continuous random
variables. A comprehensive convergence theory is included as well.
We further report numerical results with the so-called picnic
vender decision problem.