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Computational Assessment of Nested Benders and Augmented Lagrangian Decomposition for Mean-Variance Multistage Stochastic Problems

Department of Computing, Imperial College, London SW7 2AZ, United Kingdom
Department of Computing, Imperial College, London SW7 2AZ, United Kingdom
pp500{at}doc.ic.ac.uk
br{at}doc.ic.ac.uk

We consider decomposition approaches for the solution of multistage stochastic programs that appear in financial applications. In particular, we discuss the performance of two algorithms that we test on the mean-variance portfolio optimization problem. The first algorithm is based on a regularized version of Benders decomposition, and we discuss its extension to the quadratic case. The second algorithm is an augmented lagrangian method. Our results indicate that the algorithm based on regularized Benders decomposition is more efficient, which is in line with similar studies performed in the linear setting.

Key words: stochastic programming; large-scale optimization; quadratic programming; mean-variance optimization
History: received June 2003; revised August 2005; accepted September 2005.