Average curvature FISTA for nonconvex smooth composite optimization problems

Jiaming Liang () and Renato D. C. Monteiro ()
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Jiaming Liang: Yale University
Renato D. C. Monteiro: Georgia Institute of Technology

Computational Optimization and Applications, 2023, vol. 86, issue 1, No 8, 275-302

Abstract: Abstract A previous authors’ paper introduces an accelerated composite gradient (ACG) variant, namely AC-ACG, for solving nonconvex smooth composite optimization (N-SCO) problems. In contrast to other ACG variants, AC-ACG estimates the local upper curvature of the N-SCO problem by using the average of the observed upper-Lipschitz curvatures obtained during the previous iterations, and uses this estimation and two composite resolvent evaluations to compute the next iterate. This paper presents an alternative FISTA-type ACG variant, namely AC-FISTA, which has the following additional features: (i) it performs an average of one composite resolvent evaluation per iteration; and (ii) it estimates the local upper curvature by using the average of the previously observed upper (instead of upper-Lipschitz) curvatures. These two properties acting together yield a practical AC-FISTA variant which substantially outperforms earlier ACG variants, including the AC-ACG variants discussed in the aforementioned authors’ paper.

Keywords: Nonconvex smooth composite optimization; Average curvature; Accelerated composite gradient methods; FISTA; First-order methods; Line search free methods; 49M05; 49M37; 65K05; 68Q25; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-023-00490-3

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