Search

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