Self-concordance and Decomposition-based Interior Point Methods for the Two-stage Stochastic Convex Optimization Problem

Authors:
Michael Chen;Sanjay Mehrotra
Affiliations:
chensy@math.yorku.ca;mehrotra@iems.northwestern.edu
Venue:
SIAM Journal on Optimization
Year:
2011

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Abstract

We study the two-stage stochastic convex optimization problem whose first- and second-stage feasible regions admit a self-concordant barrier. We show that the barrier recourse functions and the composite barrier functions for this problem form self-concordant families. These results are used to develop prototype primal interior point decomposition algorithms that are more suitable for a heterogeneous distributed computing environment. We show that the worst case iteration complexity of the proposed algorithms is the same as that for the short- and long-step primal interior algorithms applied to the extensive formulation of this problem. The generality of our results allows the possibility of using barriers other than the standard log-barrier in an algorithmic framework.