Solving polynomial least squares problems via semidefinite programming relaxations

A polynomial optimization problem whose objective function is represented as a sum of positive and even powers of polynomials, called a polynomial least squares problem, is considered. Methods to transform a polynomial least squares problem to polynomial semidefinite programs to reduce degrees of the polynomials are discussed. Computational efficiency of solving the original polynomial least squares problem and the transformed polynomial semidefinite programs is compared. Numerical results on selected polynomial least squares problems show better computational performance of a transformed polynomial semidefinite program, especially when degrees of the polynomials are larger.