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Average curvature FISTA for nonconvex smooth composite optimization problems

Author

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  • Jiaming Liang

    (Yale University)

  • Renato D. C. Monteiro

    (Georgia Institute of Technology)

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.

Suggested Citation

  • Jiaming Liang & Renato D. C. Monteiro, 2023. "Average curvature FISTA for nonconvex smooth composite optimization problems," Computational Optimization and Applications, Springer, vol. 86(1), pages 275-302, September.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:1:d:10.1007_s10589-023-00490-3
    DOI: 10.1007/s10589-023-00490-3
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    References listed on IDEAS

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    1. Jiaming Liang & Renato D. C. Monteiro & Chee-Khian Sim, 2021. "A FISTA-type accelerated gradient algorithm for solving smooth nonconvex composite optimization problems," Computational Optimization and Applications, Springer, vol. 79(3), pages 649-679, July.
    2. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    3. Weiwei Kong & Renato D. C. Monteiro, 2022. "Accelerated inexact composite gradient methods for nonconvex spectral optimization problems," Computational Optimization and Applications, Springer, vol. 82(3), pages 673-715, July.
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