SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs

We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class of convex quadratic relaxations which are derived via quadratic cuts. To construct these quadratic cuts, we solve a separation problem involving a linear matrix inequality with a special structure that allows the use of … Read more

Spectral relaxations and branching strategies for global optimization of mixed-integer quadratic programs

We consider the global optimization of nonconvex quadratic programs and mixed-integer quadratic programs. We present a family of convex quadratic relaxations which are derived by convexifying nonconvex quadratic functions through perturbations of the quadratic matrix. We investigate the theoretical properties of these quadratic relaxations and show that they are equivalent to some particular semidefinite programs. … Read more

On the impact of running intersection inequalities for globally solving polynomial optimization problems

We consider global optimization of nonconvex problems whose factorable reformulations contain a collection of multilinear equations. Important special cases include multilinear and polynomial optimization problems. The multilinear polytope is the convex hull of a set of binary points satisfying a number of multilinear equations. Running intersection inequalities are a family of facet-defining inequalities for the … Read more

QPLIB: A Library of Quadratic Programming Instances

This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very “varied” class of problems, comprising sub-classes of problems ranging from trivial to undecidable. Solution methods for QP are very diverse, ranging … Read more