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A Decomposition Method for Large Scale MILPs, with Performance Guarantees and a Power System Application


R. Vujanic, P. Mohajerin Esfahani, P.J. Goulart, S. Mariéthoz, M. Morari

Automatica, vol. 67, pp. 144-156, (arXiv:1411.1973)


Lagrangian duality in mixed integer optimization is a useful framework for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce optimal solutions directly. In fact, solutions recovered from the dual may be not only suboptimal, but even infeasible. In this paper we concentrate on large-scale mixed integer programs with a specific structure that is of widespread practical interest, as it appears in a variety of application domains such as power systems or supply chain management. Based on geometric properties of the primal solutions recovered, we propose a solution method in which the primal problem is modified in a certain way, guaranteeing that the solutions produced by the corresponding dual are feasible for the original unmodified primal problem. The modification is simple to implement and the method is amenable to distributed computations. We also demonstrate that the quality of the solutions recovered using our procedure improves as the problem size increases, making it particularly useful for large scale instances for which commercial solvers are inadequate. We illustrate the efficacy of our method with extensive experimentations on a problem stemming from power systems.


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% Autogenerated BibTeX entry
@Article { VujEtal:2016:IFA_4587,
    author={R. Vujanic and P. Mohajerin Esfahani and P.J. Goulart and S.
	  Mari{\'e}thoz and M. Morari},
    title={{A Decomposition Method for Large Scale MILPs, with
	  Performance Guarantees and a Power System Application}},
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