2008-07-05Buch DOI: 10.18452/3021
Convergence Analysis of a Weighted Barrier Decomposition Algorithm for Two Stage Stochastic Programming
Ozevin, M. Gokhan
Mehrotra and Ozevin  computationally found that a weighted primal barrier decomposition algorithm signiﬁcantly outperforms the barrier decomposition proposed and analyzed in [11; 6; 8]. This paper provides a theoretical foundation for the weighted barrier decomposition algorithm (WBDA) in . Although the worst case analysis of the WBDA achieves a ﬁrst-stage iteration complexity bound that is worse than the bound shown for the decomposition algorithms of  and [6; 8], under a probabilistic assumption we show that the worst case iteration complexity of WBDA is independent of the number of scenarios in the problem. The probabilistic assumption uses a novel concept of self-concordant random variables.
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