In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field...

We construct convex, semidefinite programming (SDP) relaxations of the convex hull of association schemes with given parameters. As an application, we obtain new and known SDP relaxations of several combinatorial optimizations problems, including the traveling salesman and cycle covering...

We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E....