Random Coordinate Minimization Method with Eventual Transverse Directions for Constrained Polynomial Optimization

in this paper, we propose a novel algorithm for the solution of polynomial optimization problems. In particular, we show that, under mild assumptions, such problems can be solved by performing a random coordinate-wise minimization and, eventually, when a coordinate-wise minimum has been reached, an univariate minimization along a randomly chosen direction. The theoretical results are corroborated by a numerical example where the given procedure is compared with several other methods able to solve polynomial problems.