Scenario Formulation of Stochastic Linear Programs and the Homogeneous Self-Dual Interior-Point Method

Authors:
Jie Sun;Xinwei Liu
Affiliations:
Department of Decision Sciences and the Singapore-MIT Alliance, National University of Singapore, Republic of Singapore;Department of Applied Mathematics, Hebei University of Technology, Tianjin, China, and Department of Decision Sciences, National University of Singapore, Republic of Singapore
Venue:
INFORMS Journal on Computing
Year:
2006

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Abstract

We consider a homogeneous self-dual interior-point algorithm for solving multistage stochastic linear programs. The algorithm is particularly suitable for the so-called “scenario formulation” of the problem, whose constraint system consists of a large block-diagonal matrix together with a set of sparse nonanticipativity constraints. Due to this structure, the major computational work required by the homogeneous self-dual interior-point method can be split into three steps, each of which is highly decomposable. Numerical results on some randomly generated problems and a multistage production-planning problem are reported.