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SPEPS Preprint

Author(s): Sanjay Mehrotra, Northwestern University, Evanston
M. Gokhan Ozevin, Northwestern University, Evanston
Title: Convergence Analysis of a Weighted Barrier Decomposition Algorithm for Two Stage Stochastic Programming
Date of Acceptance: 05.07.2008
Submission Date: 01.03.2008
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint: pdf (urn:nbn:de:kobv:11-10090107)
Keywords (eng): two stage stochastic programming, linear-quadratic programming, Bender's decomposition, lagre scale optimization, nondifferentiable convex optimization
Appeared in: Technical Report 07 (2007)
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Abstract (eng):
Mehrotra and Ozevin [7] 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 [7]. 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 [11] 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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