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Cuts for mixed 0-1 conic programming

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Abstract

In this we paper we study techniques for generating valid convex constraints for mixed 0-1 conic programs. We show that many of the techniques developed for generating linear cuts for mixed 0-1 linear programs, such as the Gomory cuts, the lift-and-project cuts, and cuts from other hierarchies of tighter relaxations, extend in a straightforward manner to mixed 0-1 conic programs. We also show that simple extensions of these techniques lead to methods for generating convex quadratic cuts. Gomory cuts for mixed 0-1 conic programs have interesting implications for comparing the semidefinite programming and the linear programming relaxations of combinatorial optimization problems, e.g. we show that all the subtour elimination inequalities for the traveling salesman problem are rank-1 Gomory cuts with respect to a single semidefinite constraint. We also include results from our preliminary computational experiments with these cuts.

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Authors and Affiliations

  1. GERAD and Départment d’Informatique et de Recherche Opérationnelle, Université de Montréal, Montréal, H3C 3J7, Canada

    M.T. Çezik

  2. IEOR Department, Columbia University New York, New York, 10027, USA

    G. Iyengar

Authors
  1. M.T. Çezik
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  2. G. Iyengar
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Correspondence to G. Iyengar.

Additional information

Research partially supported by NSF grants CCR-00-09972, DMS-01-04282 and ONR grant N000140310514.

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Çezik, M., Iyengar, G. Cuts for mixed 0-1 conic programming. Math. Program. 104, 179–202 (2005). https://doi.org/10.1007/s10107-005-0578-3

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