Abstract
In this paper we propose an adaptively extrapolated proximal gradient method, which is based on the accelerated proximal gradient method (also known as FISTA); however, we locally optimize the extrapolation parameter by carrying out an exact (or inexact) line search. It turns out that in some situations, the proposed algorithm is equivalent to a class of SR1 (identity minus rank 1) proximal quasi-Newton methods. Convergence is proved in a general nonconvex setting, and hence, as a byproduct, we also obtain new convergence guarantees for proximal quasi-Newton methods. The efficiency of the new method is shown in numerical experiments on a sparsity regularized nonlinear inverse problem.
Originalsprache | englisch |
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Seiten (von - bis) | 2482-2503 |
Seitenumfang | 22 |
Fachzeitschrift | SIAM Journal on Optimization |
Jahrgang | 29 |
Ausgabenummer | 4 |
DOIs | |
Publikationsstatus | Veröffentlicht - 1 Jan. 2019 |
ASJC Scopus subject areas
- Software
- Theoretische Informatik