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

The augmented Lagrangian method can be used for solving recourse problemsand obtaining their normal solution in solving two-stage stochastic linearprogramming problems. The augmented Lagrangian objective function ofa stochastic linear problem is not twice differentiable which precludes theuse of a Newton method. In this paper, we apply the smoothing techniquesand a fast Newton-Armijo algorithm for solving an unconstrained smoothreformulation of this problem. Computational results and comparisons aregiven to show the effectiveness and speed of the algorithm