# American Institute of Mathematical Sciences

January  2005, 1(1): 99-122. doi: 10.3934/jimo.2005.1.99

## A class of stochastic mathematical programs with complementarity constraints: reformulations and algorithms

 1 Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China 2 Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

Received  May 2004 Revised  November 2004 Published  January 2005

We consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs), in which all decisions are required to be made here-and-now, before a random event is observed. We show that this kind of SMPEC plays a very important role in practice. In order to develop effective algorithms, we first give some reformulations of the SMPEC and then, based on these reformulations, we propose a smoothed penalty approach for solving the problem. A comprehensive convergence theory is also included.
Citation: Gui-Hua Lin, Masao Fukushima. A class of stochastic mathematical programs with complementarity constraints: reformulations and algorithms. Journal of Industrial & Management Optimization, 2005, 1 (1) : 99-122. doi: 10.3934/jimo.2005.1.99
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