A Variation on a Random Coordinate Minimization Method for Constrained Polynomial Optimization

In this paper, an algorithm is proposed for solving constrained and unconstrained polynomial minimization problems. The algorithm is a variation on random coordinate descent, in which transverse steps are seldom taken. Differently from other methods available in the literature, the proposed technique is guaranteed to converge in probability to the global solution of the minimization problem, even when the objective polynomial is nonconvex. The theoretical results are corroborated by a complexity analysis and by numerical tests that validate its efficiency.