A New Decomposition Technique in Solving Multistage Stochastic Linear Programs by Infeasible Interior Point Methods

Authors:
Xinwei Liu;Jie Sun
Affiliations:
Department of Decision Sciences, National University of Singapore, and Faculty of Science and Arts, Hebei University of Technology, Tianjin, China (e-mail: smaliuxw@nus.edu.sg;Department of Decision Sciences and Singapore-MIT Alliance, National University of Singapore (e-mail: jsun@nus.edu.sg
Venue:
Journal of Global Optimization
Year:
2004

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Abstract

Multistage stochastic linear programming (MSLP) is a powerful tool for making decisions under uncertainty. A deterministic equivalent problem of MSLP is a large-scale linear program with nonanticipativity constraints. Recently developed infeasible interior point methods are used to solve the resulting linear program. Technical problems arising from this approach include rank reduction and computation of search directions. The sparsity of the nonanticipativity constraints and the special structure of the problem are exploited by the interior point method. Preliminary numerical results are reported. The study shows that, by combining the infeasible interior point methods and specific decomposition techniques, it is possible to greatly improve the computability of multistage stochastic linear programs.