A parallel interior point decomposition algorithm for block angular semidefinite programs
Computational Optimization and Applications
SIAM Journal on Optimization
A preconditioning technique for Schur complement systems arising in stochastic optimization
Computational Optimization and Applications
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We introduce two-stage stochastic semidefinite programs with recourse and present an interior point algorithm for solving these problems using Bender’s decomposition. This decomposition algorithm and its analysis extend Zhao’s results [Math. Program., 90 (2001), pp. 507-536] for stochastic linear programs. The convergence results are proved by showing that the logarithmic barrier associated with the recourse function of two-stage stochastic semidefinite programs with recourse is a strongly self-concordant barrier on the first stage solutions. The short-step variant of the algorithm requires $O(\sqrt{p+Kr} \ln \mu^0/\epsilon)$ Newton iterations to follow the first stage central path from a starting value of the barrier parameter $\mu^0$ to a terminating value &egr;. The long-step variant requires $O((p+Kr) \ln \mu^0/\epsilon)$ damped Newton iterations. The calculation of the gradient and Hessian of the recourse function and the first stage Newton direction decomposes across the second stage scenarios.