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

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