The augmented system variant of IPMs in two--stage stochastic linear programming computation

Csaba Meszaros

The application of interior point methods (IPM) to solve the deterministic equivalent of two--stage stochastic linear programming problems is a known and natural idea. Experiments show that among the interior point methods, the augmented system approach gives the best performance on these problems. However, most of their implementations encounter numerical difficulties in certain cases, which can result in losing the efficiency. We present our augmented system solver which ``automatically'' exploits the special behavior of the problems. We investigate special properties of the augmented system which make its use fast and numerically robust. We demonstrate our method by solving a number of large--scale two--stage stochastic linear programming problems, and we compare our solver with {\sf fo1aug} \cite{fourer-mehrotra:93} which is considered as a state--of--the--art augmented system implementation of interior point methods.

Working Paper WP 95-11, Computer and Automation Institute, Hungarian Academy of Sciences, Budapest.