On complexity and convergence of high-order coordinate descent algorithms for smooth nonconvex box-constrained minimization

Coordinate descent methods have considerable impact in global optimization because (or, at least, almost global) minimization is affordable for low-dimensional problems. with high-order regularized models smooth nonconvex box-constrained are introduced this work. High-order stationarity asymptotic convergence and first-order worst-case evaluation complexity bounds established. The computer work that necessary obtaining $\varepsilon$-stationarity respect to the variables of each coordinate-descent block $O(\varepsilon^{-(p+1)/p})$ whereas getting all simultaneously $O(\varepsilon^{-(p+1)})$. Numerical examples involving multidimensional scaling problems presented. numerical performance enhanced by means strategies choosing initial points.