On the computation of weighted analytic centers and dual ellipsoids with the projective algorithm
Mathematical Programming: Series A and B
A cutting plane algorithm for convex programming that uses analytic centers
Mathematical Programming: Series A and B
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
A convex-analysis perspective on disjunctive cuts
Mathematical Programming: Series A and B
Acceleration of cutting-plane and column generation algorithms: Applications to network design
Networks - Special Issue on Multicommodity Flows and Network Design
Valid inequalities for mixed integer linear programs
Mathematical Programming: Series A and B
Operations Research Letters
Lift-and-project cuts for mixed integer convex programs
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
On the solution of a graph partitioning problem under capacity constraints
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
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Cutting plane methods are widely used for solving convex optimization problems and are of fundamental importance, e.g., to provide tight bounds for Mixed-Integer Programs (MIPs). This is obtained by embedding a cut-separation module within a search scheme. The importance of a sound search scheme is well known in the Constraint Programming (CP) community. Unfortunately, the “standard” search scheme typically used for MIP problems, known as the Kelley method, is often quite unsatisfactory because of saturation issues. In this paper we address the so-called Lift-and-Project closure for 0-1 MIPs associated with all disjunctive cuts generated from a given set of elementary disjunction. We focus on the search scheme embedding the generated cuts. In particular, we analyze a general meta-scheme for cutting plane algorithms, called in-out search, that was recently proposed by Ben-Ameur and Neto [1]. Computational results on test instances from the literature are presented, showing that using a more clever meta-scheme on top of a black-box cut generator may lead to a significant improvement.