Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.cam.2009.12.050
Title: On the implementation of a log-barrier progressive hedging method for multistage stochastic programs
Authors: Liu, X.
Toh, K.-C. 
Zhao, G. 
Keywords: Lagrangian dual
Log-barrier method
Multistage stochastic programs
Progressive hedging method
Issue Date: 15-May-2010
Source: Liu, X., Toh, K.-C., Zhao, G. (2010-05-15). On the implementation of a log-barrier progressive hedging method for multistage stochastic programs. Journal of Computational and Applied Mathematics 234 (2) : 579-592. ScholarBank@NUS Repository. https://doi.org/10.1016/j.cam.2009.12.050
Abstract: A progressive hedging method incorporated with self-concordant barrier for solving multistage stochastic programs is proposed recently by Zhao [G. Zhao, A Lagrangian dual method with self-concordant barrier for multistage stochastic convex nonlinear programming, Math. Program. 102 (2005) 1-24]. The method relaxes the nonanticipativity constraints by the Lagrangian dual approach and smoothes the Lagrangian dual function by self-concordant barrier functions. The convergence and polynomial-time complexity of the method have been established. Although the analysis is done on stochastic convex programming, the method can be applied to the nonconvex situation. We discuss some details on the implementation of this method in this paper, including when to terminate the solution of unconstrained subproblems with special structure and how to perform a line search procedure for a new dual estimate effectively. In particular, the method is used to solve some multistage stochastic nonlinear test problems. The collection of test problems also contains two practical examples from the literature. We report the results of our preliminary numerical experiments. As a comparison, we also solve all test problems by the well-known progressive hedging method. © 2010 Elsevier B.V. All rights reserved.
Source Title: Journal of Computational and Applied Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/103807
ISSN: 03770427
DOI: 10.1016/j.cam.2009.12.050
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