A statistical generalized programming algorithm for stochastic optimization problems

In this paper, we are concerned with an algorithm which combines the generalized linear programming technique proposed by Dantzig and Wolfe with the stochastic quasigradient method in order to solve stochastic programs with recourse. In this way, we overcome the difficulties arising in finding the exact values of the objective function of recourse problems by replacing them with the statistical estimates of the function. We present the basic steps of the proposed algorithm focusing our attention on its implementation alternatives aimed at improving both the convergence and computational performances. The main application areas are mentioned and some computational experience in the validation of our approach is reported. Finally, we discuss the possibilities of parallelization of the proposed algorithmic schemes