Asymptotic theory for solutions in statistical estimation and stochastic programming
Mathematics of Operations Research
Asymptotic behavior of optimal solutions in stochastic programming
Mathematics of Operations Research
Scaling, shifting and weighting in interior-point methods
Computational Optimization and Applications - Special issue dedicated to George Dantzig
Solving Stochastic Linear Programs with Restricted RecourseUsing Interior Point Methods
Computational Optimization and Applications
INFORMS Journal on Computing
Decomposition-Based Interior Point Methods for Two-Stage Stochastic Semidefinite Programming
SIAM Journal on Optimization
SIAM Journal on Optimization
A parallel interior point decomposition algorithm for block angular semidefinite programs
Computational Optimization and Applications
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Mehrotra and Özevin [SIAM J. Optim., 19 (2009), pp. 1846-1880] computationally found that a weighted primal barrier decomposition algorithm significantly outperforms the equally weighted barrier decomposition proposed and analyzed in [G. Zhao, Math. Program., 90 (2001), pp. 507-536; S. Mehrotra and M. G. Özevin, Oper. Res., 57 (2009), pp. 964-974; S. Mehrotra and M. G. Özevin, SIAM J. Optim., 18 (2007), pp. 206-222]. Here we consider a weighted barrier that allows us to analyze iteration complexity of algorithms in all of the aforementioned publications in a unified framework. In particular, we prove self-concordance parameter values for the weighted barrier and using these values give a worst-case iteration complexity bound for the weighted decomposition algorithm.