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Journal of Applied Mathematics
Volume 2013, Article ID 735916, 8 pages
Research Article

Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 416351914 Rasht, Iran

Received 1 February 2013; Accepted 22 April 2013

Academic Editor: Neal N. Xiong

Copyright © 2013 Saeed Ketabchi and Malihe Behboodi-Kahoo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The augmented Lagrangian method can be used for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The augmented Lagrangian objective function of a stochastic linear problem is not twice differentiable which precludes the use of a Newton method. In this paper, we apply the smoothing techniques and a fast Newton-Armijo algorithm for solving an unconstrained smooth reformulation of this problem. Computational results and comparisons are given to show the effectiveness and speed of the algorithm.