- Title
- Extrapolated proximal subgradient algorithms for nonconvex and nonsmooth fractional programs
- Creator
- Bot, Radu; Dao, Minh; Li, Guoyin
- Date
- 2022
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/190056
- Identifier
- vital:17514
- Identifier
-
https://doi.org/10.1287/moor.2021.1214
- Identifier
- ISSN:0364-765X (ISSN)
- 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. Copyright: © 2021 INFORMS.
- Publisher
- INFORMS Inst.for Operations Res.and the Management Sciences
- Relation
- Mathematics of Operations Research Vol. 47, no. 3 (2022), p. 2415-2443
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © 2021 INFORMS
- Rights
- Open Access
- Subject
- 4901 Applied mathematics; Descent method; Extrapolation; Fractional program; Kurdyka–Łojasiewicz property; Linear convergence; Proximal subgradient algorithm
- Full Text
- Reviewed
- Funder
- R. I. Bot was partially supported by the Austrian Science Fund [Project I 2419-N32]. M. N. Dao and G. Li were partially supported by the Australian Research Council [Project DP190100555].
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