Mathematical Programming

, Volume 104, Issue 1, pp 179–202

Cuts for mixed 0-1 conic programming

Article

DOI: 10.1007/s10107-005-0578-3

Cite this article as:
Çezik, M. & Iyengar, G. Math. Program. (2005) 104: 179. doi:10.1007/s10107-005-0578-3

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.GERAD and Départment d’Informatique et de Recherche OpérationnelleUniversité de MontréalMontréalCanada
  2. 2.IEOR DepartmentColumbia University New YorkNew YorkUSA