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Jiaming Liang (jiaming.lianggatech.edu) Abstract: In this paper, we describe and establish iterationcomplexity 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 wellknown 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 as input a pair (M,m), M being a Lipschitz constant of ∇f and m being a lower curvature of f such that m ≤ M (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. Keywords: Nonconvex Optimization, IterationComplexity, FirstOrder Accelerated Method, Proximal Point Method Category 1: Nonlinear Optimization Category 2: Convex and Nonsmooth Optimization Citation: Download: [PDF] Entry Submitted: 05/16/2019 Modify/Update this entry  
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