Lagrangean decomposition for large-scale two-stage stochastic mixed 0-1 problems

Laureano F. Escudero Bueno, María Araceli Garín Martín, Gloria Pérez Sainz de Rozas and Aitziber Unzueta Inchaurbe

No 1134-8984, BILTOKI from Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística)

Abstract: In this paper we study solution methods for solving the dual problem corresponding to the Lagrangean Decomposition of two stage stochastic mixed 0-1 models. We represent the two stage stochastic mixed 0-1 problem by a splitting variable representation of the deterministic equivalent model, where 0-1 and continuous variables appear at any stage. Lagrangean Decomposition is proposed for satisfying both the integrality constraints for the 0-1 variables and the non-anticipativity constraints. We compare the performance of four iterative algorithms based on dual Lagrangean Decomposition schemes, as the Subgradient method, the Volume algorithm, the Progressive Hedging algorithm and the Dynamic Constrained Cutting Plane scheme. We test the conditions and properties of convergence for medium and large-scale dimension stochastic problems. Computational results are reported.

Keywords: Lagrangean decomposition; subgradient method; volume algorithm; Progressive Hedging algorithm (search for similar items in EconPapers)
Date: 2010-07
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Dpto. de Econometría y Estadística, Facultad de CC. Económicas y Empresariales, Universidad del País Vasco, Avda. Lehendakari Aguirre 83, 48015 Bilbao, Spain

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