Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models. Often, it is known beforehand, that the underlying unknown function has certain properties, e.g., nonnegative or increasing on a certain region....

We consider the orthoganality graph omega(n) with 2n vertices corresponding to the vectors {0,1}n, two vertices adjacent if and only if the Hamming distance between them is n/2. We show that, for n=16, the stability number of omega(n) is alpha(omega(16))=2304, thus proving a conjecture by...

The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO). It is NPhard, and contains the maximum stable set problem in graphs as a special case. In this note we show that the SQO problem may be reformulated as an...

Semidefinite programming (SDP) may be viewed as an extension of linear programming (LP), and most interior point methods (IPM s) for LP can be extended to solve SDP problems. However, it is far more difficult to exploit data structures (especially sparsity) in the SDP case. In this paper we will...

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 the orthogonality graph (n) with 2n vertices corresponding to the vectors {0, 1}n, two vertices adjacent if and only if the Hamming distance between them is n/2.We show that, for n = 16, the stability number of (n) is ( (16)) = 2304, thus proving a conjecture by Galliard [7].The main...

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...

Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However,...

AMS classifications: 65D05; 65K05; 90C22;