This paper shows how the stability number can be computed as the solution of a conic linear program (LP) over the cone of copositive matrices of a graph by solving semidefinite programs (SDPs) of increasing size (lift-and-project method).Expand

The Primal Logarithmic Barrier Method and Primal-Dual Affine-Scaling Methods are presented, as well as some alternative methods for reducing the number of coefficients in a graph, using the Lovasz upsilon function.Expand

The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear… Expand

This paper shows how to approximate the optimal solution by approximating the cone of copositive matrices via systems of linear inequalities, and, more refined, linear matrix inequalities (LMI's).Expand

A general technique to reduce the size ofSemidefinite programming problems on which a permutation group is acting is described, based on a low-order matrix based on the representation of the commutant (centralizer ring) of the matrix algebra generated by the permutation matrices.Expand

It is shown that in the univariate case (n = 1), these problems have exact reformulations as semidefinite programming (SDP) problems, by using reformulations introduced in the PhD thesis of Jibetean [16].Expand

We consider the problem of minimizing a polynomial on the hypercube $[0,1]^n$ and derive new error bounds for the hierarchy of semidefinite programming approximations to this problem corresponding to… Expand

Improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values are shown, obtained as a consequence of the new bound on $\Cr(\ksn) 2.1796n^2 - 4.5n".Expand