This paper proves that nonconvex quadratically constrained quadratic programs can be
solved in polynomial time when their underlying graph is acyclic, provided the constraints …

We study the generalization of split, k-branch split, and intersection cuts from mixed integer
linear programming to the realm of mixed integer nonlinear programming. Constructing such …

A great deal of research has been focusing, since the early seventies, on finding strong
relaxations for the stable set problem. Polyhedral combinatorics techniques have been at …

The principal idea of this paper is to exploit Semidefinite Programming (SDP) relaxation
within the framework provided by Mixed Integer Nonlinear Programming (MINLP) solvers …

A new exact approach to the stable set problem is presented, which attempts to avoid the
pitfalls of existing approaches based on linear and semidefinite programming. The method …

One of the most important breakthroughs in the area of Mixed Integer Linear Programming
(MILP) is the characterization of the convex hull of specially structured non-convex …

The famous Lovász theta number θ (G) is expressed as the optimal solution of a semidefinite
program. As such, it can be computed in polynomial time to an arbitrary precision …

A uadratically constrained quadratic programming (QCQP) problem is to minimize a
quadratic objective function subject to quadratic equality and/or inequality constraints where …

When addressing the maximum stable set problem on a graph G=(V, E), rank inequalities
prescribe that, for any subgraph G [U] induced by U⊆ V, at most as many vertices as the …

A great deal of research has been focusing, since the early seventies, on finding strong
relaxations for the stable set problem. Polyhedral combinatorics techniques have been at …