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Corner polyhedron and intersection cuts
Four decades ago, Gomory introduced the corner polyhedron as a relaxation of a mixed
integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron …
integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron …
Theoretical challenges towards cutting-plane selection
While many classes of cutting-planes are at the disposal of integer programming solvers, our
scientific understanding is far from complete with regards to cutting-plane selection, ie, the …
scientific understanding is far from complete with regards to cutting-plane selection, ie, the …
Valid inequalities for structured integer programs
In Chaps. 5 and 6 we have introduced several classes of valid inequalities that can be used
to strengthen integer programming formulations in a cutting plane scheme. All these valid …
to strengthen integer programming formulations in a cutting plane scheme. All these valid …
On the facets of mixed integer programs with two integer variables and two constraints
In this paper we consider an infinite relaxation of the mixed integer linear program with two
integer variables, nonnegative continuous variables and two equality constraints, and we …
integer variables, nonnegative continuous variables and two equality constraints, and we …
Round-robin tournaments generated by the circle method have maximum carry-over
Abstract The Circle Method is widely used in the field of sport scheduling to generate
schedules for round-robin tournaments. If in such a tournament, team A played team B in its …
schedules for round-robin tournaments. If in such a tournament, team A played team B in its …
A -Slope Theorem for the -Dimensional Infinite Group Relaxation
We prove that any minimal valid function for the k-dimensional infinite group relaxation that
is continuous piecewise linear with at most k+1 slopes and does not factor through a linear …
is continuous piecewise linear with at most k+1 slopes and does not factor through a linear …
The group-theoretic approach in mixed integer programming
In this chapter, we provide an overview of the mathematical foundations and recent
theoretical and computational advances in the study of the grouptheoretic approach in …
theoretical and computational advances in the study of the grouptheoretic approach in …
A geometric approach to cut-generating functions
The cutting-plane approach to integer programming was initiated more than 40 years ago:
Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau …
Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau …
On degenerate multi-row Gomory cuts
Borozan and Cornuéjols show that valid inequalities for an infinite relaxation for MIPs,
relative to some vertex f of the linear relaxation, are determined by maximal lattice-free …
relative to some vertex f of the linear relaxation, are determined by maximal lattice-free …
Nonunique lifting of integer variables in minimal inequalities
We explore the lifting question in the context of cut-generating functions. Most of the prior
literature on this question focuses on cut-generating functions that have the unique lifting …
literature on this question focuses on cut-generating functions that have the unique lifting …