Solving moment and polynomial optimization problems on Sobolev spaces

Using standard tools of harmonic analysis, we state and solve the problem of moments for positive measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner semidefinite approximations of the cone of Sobolev moments. They are the basic components of an infinite-dimensional moment-sums of squares … Read more

Global optimization on the torus, the sphere and the rotation group

Detecting all local extrema or the global extremum of a polynomial on the torus, the sphere or the rotation group is a tough yet often requested numerical problem. We present a heuristic approach that applies common descent methods like nonlinear conjugated gradients or Newtons methods simultaneously to a large number of starting points. The corner … Read more

Lecture notes: Semidefinite programs and harmonic analysis

Lecture notes for the tutorial at the workshop HPOPT 2008 – 10th International Workshop on High Performance Optimization Techniques (Algebraic Structure in Semidefinite Programming), June 11th to 13th, 2008, Tilburg University, The Netherlands. Citation arXiv:0809.2017v1 [math.OC] Article Download View Lecture notes: Semidefinite programs and harmonic analysis