On interior-point based retrospective approximation methods for solving two-stage stochastic linear programs

In a recent paper, Gongyun Zhao introduced what appears to be the first interior point formulation for solving two-stage stochastic linear programs for finite support random variables. In this paper, we generalize Gongyun Zhao's formulation by incorporating it into a retrospective approximation framework. What results is an implementable interior-point solution paradigm that can be used to solve general two-stage stochastic linear programs. After discussing some basic properties, we characterize the complexity of the algorithm, leading to guidance on the number of samples that should be generated to construct the sub-problem linear programs, effort expended in solving the sub-problems, and the effort expended in solving the master problem.