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

Jiaming Liang (), Renato D. C. Monteiro () and Chee-Khian Sim ()
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Jiaming Liang: Georgia Institute of Technology
Renato D. C. Monteiro: Georgia Institute of Technology
Chee-Khian Sim: University of Portsmouth

Computational Optimization and Applications, 2021, vol. 79, issue 3, No 5, 649-679

Abstract: 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

Date: 2021
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DOI: 10.1007/s10589-021-00280-9

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