The abbreviations LMI and SOS stand for “linear matrix inequality" and “sum of squares,"
respectively. The cone n,2d of SOS polynomials in n variables of degree at most 2d is known …

Let A be an m× n matrix with nonnegative real entries. The psd rank of A is the smallest k for
which there exist two families (P 1,…, P m) and (Q 1,…, Q n) of positive semidefinite …

In convex integer programming, various procedures have been developed to strengthen
convex relaxations of sets of integer points. On the one hand, there exist several general …

Mixed-integer mathematical programs are among the most commonly used models for a
wide set of problems in Operations Research and related fields. However, there is still very …

We show that for every A⊆{0, 1} n, there exists a polytope P⊆ R n with P∩{0, 1} n= A and
extension complexity O (2 n/2), and that there exists an A⊆{0, 1} n such that the extension …

The ground space of every element of a vector space of Hermitian matrices is an intersection
of maximal ground spaces of matrices from the same space. We characterize the ground …

There has been a series of developments in the recent literature (by essentially a
same'circle'of authors) with the absolute/unconditioned (implicit or explicit) claim that there …

In combinatorial optimization, many problems can be modeled by optimizing a linear
functional over a polyhedron, which is the feasible set of finitely many linear inequalities …

In combinatorial optimization, many problems can be modeled by optimizing a linear
functional over a polytope. The standard tool to manage such a problem is the well-known …

The ground spaces of a vector space of hermitian matrices, partially ordered by inclusion,
form a lattice constructible from top to bottom in terms of intersections of maximal ground …