Decomposition Based Interior Point Methods for Two-Stage Stochastic Convex Quadratic Programs with Recourse

Zhao [28] recently showed that the log barrier associated with the recourse function of twostage stochastic linear programs behaves as a strongly self-concordant barrier and forms a self concordant family on the first stage solutions. In this paper we show that the recourse function is also strongly self-concordant and forms a self concordant family for the two-stage stochastic convex quadratic programs with recourse. This allows us to develop Benders decomposition based linearly convergent interior point algorithms. An analysis of such an algorithm is given in this paper. ∗This research was partially supported by NSF grant DMI-0200151, and ONR grant N0014-01-10048/P00002