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

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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 ƒ with a Lipschitz continuous gradient and a simple nonsmooth closed convex function h. When ƒ 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 ƒ is m-weakly convex, ∇ƒ is M-Lipschitz continuous, and mM (possibly m < M), which is usually hard to obtain or poorly estimated. The second variant on the other hand can start from an arbitrary input pair (M, m) of positive scalars and its complexity is shown to be not worse, and better in some cases, than that of the first variant for a large range of the input pairs. Finally, numerical results are provided to illustrate the efficiency of the two ACG variants.
Original languageEnglish
Pages (from-to)649-679
Number of pages31
JournalComputational Optimization and Applications
Publication statusPublished - 13 May 2021


  • A FISTA-type accelerated gradient algorithm AAM

    Rights statement: This is a post-peer-review, pre-copyedit version of an article published in Computational Optimization and Applications. The final authenticated version is available online at:

    Accepted author manuscript (Post-print), 397 KB, PDF document

    Due to publisher’s copyright restrictions, this document is not freely available to download from this website until: 13/05/22

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