New reformulation and feasible semismooth Newton method for a class of stochastic linear complementarity problems

New reformulation and feasible semismooth Newton method for a class of stochastic linear complementarity problems

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Article ID: iaor20116408
Volume: 217
Issue: 23
Start Page Number: 9723
End Page Number: 9740
Publication Date: Aug 2011
Journal: Applied Mathematics and Computation
Authors: , ,
Keywords: stochastic processes
Abstract:

A class of stochastic linear complementarity problems (SLCPs) with finitely many realizations is considered. We first formulate the problem as a new constrained minimization problem. Then, we propose a feasible semismooth Newton method which yields a stationary point of the constrained minimization problem. We study the condition for the level set of the objective function to be bounded. As a result, the condition for the solution set of the constrained minimization problem is obtained. The global and quadratic convergence of the proposed method is proved under certain assumptions. Preliminary numerical results show that this method yields a reasonable solution with high safety and within a small number of iterations.

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