- Title
- A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems
- Creator
- Pham, Tan; Dao, Minh; Shah, Rakibuzzaman; Sultanova, Nargiz; Li, Guoyin; Islam, Syed
- Date
- 2023
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/199668
- Identifier
- vital:19259
- Identifier
-
https://doi.org/10.1007/s11075-023-01554-5
- Identifier
- ISSN:1017-1398 (ISSN)
- Abstract
- In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous gradient, subtracted by a weakly convex function. This general framework allows us to tackle problems involving nonconvex loss functions and problems with specific nonconvex constraints, and it has many applications such as signal recovery, compressed sensing, and optimal power flow distribution. We develop a proximal subgradient algorithm with extrapolation for solving these problems with guaranteed subsequential convergence to a stationary point. The convergence of the whole sequence generated by our algorithm is also established under the widely used Kurdyka–Łojasiewicz property. To illustrate the promising numerical performance of the proposed algorithm, we conduct numerical experiments on two important nonconvex models. These include a compressed sensing problem with a nonconvex regularization and an optimal power flow problem with distributed energy resources. © 2023, The Author(s).
- Publisher
- Springer
- Relation
- Numerical Algorithms Vol. 94, no. 4 (2023), p. 1763-1795
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- http://creativecommons.org/licenses/by/4.0/
- Rights
- Copyright © 2023, The Author(s)
- Subject
- 4901 Applied mathematics; 4903 Numerical and computational mathematics; Composite optimization problem; Difference of convex; Distributed energy resources; Extrapolation; Optimal power flow; Proximal subgradient algorithm
- Full Text
- Reviewed
- Funder
- Open Access funding enabled and organized by CAUL and its Member Institutions. The research of TNP was supported by Henry Sutton PhD Scholarship Program from Federation University Australia. The research of MND benefited from the FMJH Program Gaspard Monge for optimization and operations research and their interactions with data science, and was supported by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH. The research of GL was supported by Discovery Project 190100555 from the Australian Research Council.
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