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Computing deep facet-defining disjunctive cuts for mixed-integer programming

Florent Cadoux 1
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : The problem of separation is to find an affine hyperplane, or "cut", that lies between the origin O and a given closed convex set Q in a Euclidean space. We study cuts which are deep in a well-defined geometrical sense, and facet-defining. The cases when the deepest cut is decomposable as a combination of facet-defining cuts are characterized using the reverse polar set. When Q is a disjunctive polyhedron, a description of the reverse polar, linked to the so-called cut generating linear program of lift-and-project techniques, is given. A successive projections algorithm onto the reverse polar is proposed that computes the decomposition of the deepest cut into facet-defining cuts. Illustrative numerical experiments show how these cuts compare with the deepest cut, and with the most violated cut.
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Submitted on : Wednesday, June 17, 2009 - 2:36:10 PM
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Florent Cadoux. Computing deep facet-defining disjunctive cuts for mixed-integer programming. Mathematical Programming, Springer Verlag, 2010, 122 (2), pp.197-223. ⟨10.1007/s10107-008-0245-6⟩. ⟨inria-00396289⟩



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