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Smoothing Implicit Programming Approaches For Stochastic Mathematical Programs With Linear Complementarity Constraints
, 2003
"... 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 lowerlevel waitan ..."
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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 lowerlevel waitandsee and hereand now decision problems. For the lowerlevel waitandsee model, we propose a smoothing implicit programming method and establish a comprehensive convergence theory. For the hereandnow decision problem, we apply a penalty technique and suggest a similar method. We show that the two methods possess similar convergence properties.
Smooth minimization of twostage stochastic linear programs
, 2006
"... This note presents an application of the smooth optimization technique of Nesterov [7] for solving twostage stochastic linear programs. It is shown that the original O ( 1) bound of [7] on the number of ɛ main iterations required to obtain an ɛoptimal solution is retained. 1 ..."
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This note presents an application of the smooth optimization technique of Nesterov [7] for solving twostage stochastic linear programs. It is shown that the original O ( 1) bound of [7] on the number of ɛ main iterations required to obtain an ɛoptimal solution is retained. 1