Abstract
Interior point methods for multistage stochastic programs involve KKT systems with a characteristic global block structure induced by dynamic equations on the scenario tree. We generalize the recursive solution algorithm proposed in an earlier paper so that its linear complexity extends to a refined tree-sparse KKT structure. Then we analyze how the block operations can be specialized to take advantage of problem-specific sparse substructures. Savings of memory and operations for a financial engineering application are discussed in detail.
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Steinbach, M.C. (2001). Hierarchical Sparsity in Multistage Stochastic Programs. In: Uryasev, S., Pardalos, P.M. (eds) Stochastic Optimization: Algorithms and Applications. Applied Optimization, vol 54. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6594-6_16
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DOI: https://doi.org/10.1007/978-1-4757-6594-6_16
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