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A FISTA-type accelerated gradient algorithm for solving smooth nonconvex composite optimization problems

Author

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  • Jiaming Liang

    (Georgia Institute of Technology)

  • Renato D. C. Monteiro

    (Georgia Institute of Technology)

  • Chee-Khian Sim

    (University of Portsmouth)

Abstract

In this paper, we describe and establish iteration-complexity of two accelerated composite gradient (ACG) variants to solve a smooth nonconvex composite optimization problem whose objective function is the sum of a nonconvex differentiable function f with a Lipschitz continuous gradient and a simple nonsmooth closed convex function h. When f is convex, the first ACG variant reduces to the well-known FISTA for a specific choice of the input, and hence the first one can be viewed as a natural extension of the latter one to the nonconvex setting. The first variant requires an input pair (M, m) such that f is m-weakly convex, $$\nabla f$$ ∇ f is M-Lipschitz continuous, and $$m \le M$$ m ≤ M (possibly $$m

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:79:y:2021:i:3:d:10.1007_s10589-021-00280-9
    DOI: 10.1007/s10589-021-00280-9
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    1. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. 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.

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