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

V. S. Amaral (), R. Andreani (), E. G. Birgin (), D. S. Marcondes () and J. M. Martínez ()
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V. S. Amaral: University of Campinas
R. Andreani: University of Campinas
E. G. Birgin: University of São Paulo
D. S. Marcondes: University of São Paulo
J. M. Martínez: University of Campinas

Journal of Global Optimization, 2022, vol. 84, issue 3, No 1, 527-561

Abstract: Abstract 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 $$\varepsilon $$ ε -stationarity with respect to the variables of each coordinate-descent block is $$O(\varepsilon ^{-(p+1)/p})$$ O ( ε - ( p + 1 ) / p ) whereas the computer work for getting first-order $$\varepsilon $$ ε -stationarity with respect to all the variables simultaneously is $$O(\varepsilon ^{-(p+1)})$$ 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.

Keywords: Coordinate descent methods; Bound-constrained minimization; Worst-case evaluation complexity; 90C30; 65K05; 49M37; 90C60; 68Q25 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-022-01168-6

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