A statistical generalized programming algorithm for stochastic optimization problems

In this paper the authors 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, they 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. The authors present the basic steps of the proposed algorithm focusing their 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 the present approach is reported. Finally, the authors discuss the possibilities of parallelization of the proposed algorithmic schemes.