Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programs

Radu Ioan Boţ (), Minh N. Dao () and Guoyin Li ()
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Radu Ioan Boţ: Faculty of Mathematics, University of Vienna, A-1090 Vienna, Austria
Minh N. Dao: School of Engineering, Information Technology and Physical Sciences, Federation University Australia, Ballarat, Victoria 3353, Australia
Guoyin Li: Department of Applied Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia

Mathematics of Operations Research, 2022, vol. 47, issue 3, 2415-2443

Abstract: In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, which encompass many important modern optimization problems arising from diverse areas such as the recently proposed scale-invariant sparse signal reconstruction problem in signal processing. We propose a proximal subgradient algorithm with extrapolations for solving this optimization model and show that the iterated sequence generated by the algorithm is bounded and that any one of its limit points is a stationary point of the model problem. The choice of our extrapolation parameter is flexible and includes the popular extrapolation parameter adopted in the restarted fast iterative shrinking-threshold algorithm (FISTA). By providing a unified analysis framework of descent methods, we establish the convergence of the full sequence under the assumption that a suitable merit function satisfies the Kurdyka–Łojasiewicz property. Our algorithm exhibits linear convergence for the scale-invariant sparse signal reconstruction problem and the Rayleigh quotient problem over spherical constraint. When the denominator is the maximum of finitely many continuously differentiable weakly convex functions, we also propose another extrapolated proximal subgradient algorithm with guaranteed convergence to a stronger notion of stationary points of the model problem. Finally, we illustrate the proposed methods by both analytical and simulated numerical examples.

Keywords: Primary: 90C26; 90C32; secondary: 49M27; 65K05; descent method; extrapolation; fractional program; Kurdyka–Łojasiewicz property; linear convergence; proximal subgradient algorithm (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:3:p:2415-2443

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