Kybernetika 49 no. 1, 188-198, 2013

Augmented Lagrangian method for recourse problem of two-stage stochastic linear programming

Saeed Ketabchi and Malihe Behboodi-Kahoo


In this paper, the augmented Lagrangian method is investigated for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The objective function of stochastic linear programming problem is piecewise linear and non-differentiable. Therefore, to use a smooth optimization methods, the objective function is approximated by a differentiable and piecewise quadratic function. Using quadratic approximation, it is required to obtain the least 2-norm solution for many linear programming problems in each iteration. To obtain the least 2-norm solution for inner problems based on the augmented Lagrangian method, the generalized Newton method is applied.


two-stage stochastic linear programming, recourse problem, normal solution, augmented Lagrangian method


90C15, 90C05, 90C20


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