Solving Stochastic Programming Problems by Successive Regression Approximations Numerical Results* Istvan Deak 1 Operations Research Group, Dept. of Differential Equations, Budapest University of Technology and Economics, H-llll Budapest, XI. Muegyetem rkp. 3. deak@math.bme.hu Summary. Recently a heuristic procedure has been developed for solving two- stage stochastic programming problems. Using the same ideas solution algorithms are presented here for solving probabilistic constrained problems and a model fam- ily, combining probabilistic constraint and recourse, proposed by Pnlkopa. The common feature of these algorithms is that all rely on replacing the "hard" part of the problem by an easy-to-compute regression function. Numerical examples and test results are also given. 1 Introduction. Regression (or in other words least squares approximation) is a two-hundred years old tool for approximating problems, effectively reducing measurement errors [1], [12], [14], [25], [28]. In a series of recent papers [4], [6] we proposed to use regression functions for approximation in a one-dimensional subproblem of probability constrained, STABIL-type models [23], [24]. It turned out, that successive regression approximations can be used for solving one-dimensional nonlinear equations, with deterministic function values [7], [8]. Based on these results, anticipating the n-dimensional analogies of the one-dimensional techniques proved, a heuristic method has been developed for solving two-stage problems [10], [11]. Here two additional algorithms are presented for solving stochastic programming problems of probabilistic con- strained and a combined model type. The main contribution of this work is thought to be the demonstration of the fact, that the same algorithm can be used to solve these problems. Two large model-families dominate the area of stochastic programming; one of them is called the probabilistic constrained models, the other one is the two-stage or recourse type models. There exists several solution techniques for both type, but a method designed for one family can not be used to solve a problem in the other one. The proposed heuristic method - according to * Submitted for publication to Proceedings, IIASA, Laxenburg conference on Stochastic Programming, based on lectures at EURO-2000 Conference on Oper- ations Research, Budapest and IIASA conference on Stochastic Programming, 2002, Laxenburg K. Marti et al. (eds.), Dynamic Stochastic Optimization © Springer-Verlag Berlin Heidelberg 2004