Self-concordant Tree and Decomposition Based Interior Point Methods for Stochastic Convex Optimization Problem

Abstract

We consider barrier problems associated with two and multistage stochastic convex optimization problems. We show that the barrier recourse functions at any stage form a self-concordant family with respect to the barrier parameter. We also show that the complexityvalue of the first stage problem increases additively with the number of stages and scenarios. Weuse these results to propose a prototype primal interior point decomposition algorithm for thetwo-stage and multistage stochastic convex optimization problems admitting self-concordantbarriers.