A. Unzueta, M. A. Garín, L. Escudero
A Multistage Scenario Cluster Lagrangean Decomposition approach is proposed for obtaining strong lower bounds on the solution value of large-scale multistage integer-linear problems with time related stochastic dominance risk averse. The original problem is represented by a mixture of the splitting representation up to the break stage, and the compact representation for the other stages. The dualization of the nonanticipativity constraints for the variables related to the nodes in the stages to up to the break one and the relaxation of the related cross node constraints results in a model that can be decomposed into a set of independent submodels. The solution of those submodels where the dualized constraints as well as the relaxed ones are factorized by related Lagrange multipliers lead to a lower bound on the solution value of the original model. We have observed in the instances we have experimented with that the smaller the number of clusters, the stronger the lower bound provided.
Keywords: Multistage stochastic mixed 0-1 optimization, time stochastic dominance-based risk averse functional, cluster Lagrangean problem, Subgradient method, Progressive Hedging algorithm, Dynamic Constrained Cutting Plane algorithm
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WA1 Decomposition methods for Stochastic Programming
June 1, 2016 9:00 AM
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