Optimization Problems over Non-negative Polynomials with Interpolation Constraints

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.