CORE DISCUSSION PAPER 2003/34 OPTIMIZATION PROBLEMS OVER NON-NEGATIVE POLYNOMIALS WITH INTERPOLATION CONSTRAINTS Yvan HACHEZ 1 and Yurii NESTEROV 1 April 2003 Abstract Optimization problems over several cones of non-negative polynomials are described; we focus on linear constraints on the coefficients that represent interpolation constraints. For these problems, the complexity of solving the dual formulation is shown to be almost independent of the number of constraints, provided that an appropriate preprocessing has been performed. These results are also extended to non-negative matrix polynomials and to interpolation constraints on the derivatives. Keywords: convex optimization, non-negative polynomials, interpola- tion constraints. 1 CORE and INMA, Universit´ e catholique de Louvain, Belgium. E-mail: {hachez,nesterov}@core.ucl.ac.be A research fellowship from the Belgian National Fund for Scientific Research is gratefully acknowledged by the first author. This text presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Pro- gramming. The scientific responsibility is assumed by the authors.