7 citations · 16 across the 10 of their papers we have counts for
8 papers · 1 filter
Chvátal-Gomory Rounding of Eigenvector Inequalities for QCQPs
Santanu S. Dey, Nan Jiang, Aleksandr Kazachkov +2
We introduce and analyze a class of valid inequalities for nonconvex quadratically constrained optimization problems (QCQPs) which we call Eigen-CG inequalities. These inequalities…
Parametric Disjunctive Cuts for Sequences of Mixed Integer Linear Optimization Problems
Shannon Kelley, Aleksandr M. Kazachkov, Ted Ralphs
Many applications require solving sequences of related mixed-integer linear programs. We introduce a class of parametric disjunctive inequalities (PDIs), obtained by reusing the di…
Approximating value functions via corner Benders' cuts
Matheus J. Ota, Ricardo Fukasawa, Aleksandr M. Kazachkov
We introduce a novel technique to generate Benders' cuts from a conic relaxation ("corner") derived from a basis of a higher-dimensional polyhedron that we aim to outer approximate…
Machine Learning for Optimization-Based Separation of Mixed-Integer Rounding Cuts
Oscar Guaje, Arnaud Deza, Aleksandr M. Kazachkov +1
Mixed-integer rounding (MIR) cutting planes (cuts) are effective at improving the strength of a linear relaxation for mixed-integer linear programming (MIP) problems. The cuts in t…
Monoidal strengthening of simple -polyhedral disjunctive cuts
Aleksandr M. Kazachkov, Egon Balas
Disjunctive cutting planes can tighten a relaxation of a mixed-integer linear program. Traditionally, such cuts are obtained by solving a higher-dimensional linear program, whose a…
-Polyhedral Disjunctive Cuts
Egon Balas, Aleksandr M. Kazachkov
We introduce -polyhedral disjunctive cuts (VPCs) for generating valid inequalities from general disjunctions. Cuts are critical to integer programming solvers, but the…
An Abstract Model for Branch and Cut
Aleksandr M. Kazachkov, Pierre Le Bodic, Sriram Sankaranarayanan
Branch and cut is the dominant paradigm for solving a wide range of mathematical programming problems -- linear or nonlinear -- combining efficient search (via branch and bound) an…
Partial hyperplane activation for generalized intersection cuts
Aleksandr M. Kazachkov, Selvaprabu Nadarajah, Egon Balas +1
The generalized intersection cut (GIC) paradigm is a recent framework for generating cutting planes in mixed integer programming with attractive theoretical properties. We investig…