International Congress on Computational and Applied Mathematics edition:13 location:Ghent, Belguim date:07-11 July 2008
Several optimization problems covering a large number of applications can be formulated as convex optimization problems. We are interested in convex problems related to nonnegative polynomials. Nonnegative polynomials are natural to model various engineering problems. In this talk a method for solving convex optimization problems, based on the use of cutting planes is described. This method is called the Analytic Center Cutting Plane Method. For numerical stability, it is important that the nonnegative polynomials are represented with respect to a good basis. For efficiency, we use fast algorithms for finding zeros of a polynomial represented in this basis. Numerical results show the efficiency and accuracy of our new approach.