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;

We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard...

We consider the problem of minimizing a univariate function f on an interval [a, b]. When f is a polynomial, we review how this problem may be reformulated as a semidefinite programming (SDP) problem, and review how to extract all global minimizers from the solution of the SDP problem. For...

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 review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard...

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....

AMS classification: 90C22, 20Cxx, 70-08

AMS classification: 90C22, 20Cxx, 70-08