In [Euro. J. Operat. Res. 143 (2002) 452, Opt. Meth. Software 17 (2002) 383] a Riccati-based primal interior point method for multistage stochastic programmes was developed. This algorithm has several interesting features. It can solve problems with a nonlinear node-separable convex objective, local linear constraints and global linear constraints. This paper demonstrates that the algorithm can be efficiently parallelized. The solution procedure in the algorithm allows for a simple but efficient method to distribute the computations. The parallel algorithm has been implemented on a low-budget parallel computer, where we experience almost perfect linear speedup and very good scalability of the algorithm. © 2003 Elsevier Science B.V. All rights reserved.

We show that a Riccati-based Multistage Stochastic Programming solver for problems with separable convex linear/nonlinear objective developed in previous papers can be extended to solve more general Stochastic Programming problems. With a Lagrangean relaxation approach, also local and global equality constraints can be handled by the Riccati-based primal interior point solver. The efficiency of the approach is demonstrated on a 10 staged stochastic programming problem containing both local and global equality constraints. The problem has 1.9 million scenarios, 67 million variables and 119 million constraints, and was solved in 97 min on a 32 node PC cluster.

We propose a new method for certain multistage stochastic programs with linear or nonlinear objective function, combining a primal interior point approach with a linear-quadratic control problem over the scenario tree. The latter problem, which is the direction finding problem for the barrier subproblem is solved through dynamic programming using Riccati equations. In this way we combine the low iteration count of interior point methods with an efficient solver for the subproblems. The computational results are promising. We have solved a financial problem with 1,000,000 scenarios, 15,777,740 variables and 16,888,850 constraints in 20 hours on a moderate computer. © 2002 Elsevier Science B.V. All rights reserved.