Representations of Non-Negative Polynomials, Degree Bounds and Applications to Optimization
Representations of Non-Negative Polynomials, Degree Bounds and Applications to Optimization
Abstract. Natural sufficient conditions for a polynomial to have a local minimum at a point are considered. These conditions tend to hold with probability 1. It is shown that polynomials satisfying these conditions at each minimum point have nice presentations in terms of sums of squares. Applications are given to …