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A hybrid approach of bundle and Benders applied large mixed linear integer problem. (English) Zbl 1271.90049
Summary: Consider a large mixed integer linear problem where structure of the constraint matrix is sparse, with independent blocks, and coupling constraints and variables. There is one of the groups of constraints to make difficult the application of Benders scheme decomposition. In this work, we propose the following algorithm; a Lagrangian relaxation is made on the mentioned set of constraints; we presented a process heuristic for the calculation of the multiplier through the resolution of the dual problem, structured starting from the bundle methods. According to the methodology proposed, for each iteration of the algorithm, we propose Benders decomposition where quotas are provided for the value function and $$\varepsilon$$-subgradient.
Reviewer: Reviewer (Berlin)

##### MSC:
 90C05 Linear programming 90C11 Mixed integer programming
##### Software:
CPLEX; MINTO; NOA
Full Text:
##### References:
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