Scenario formulation of stochastic linear programs and the homogeneous self-dual interior-point method

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.