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http://hdl.handle.net/10397/70942
| Title: | Linear convergence of proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth minimization problems | Authors: | Wen, B Chen, X Pong, TK |
Issue Date: | 2017 | Source: | SIAM journal on optimization, 2017, v. 27, no. 1, p. 124-145 | Abstract: | In this paper, we study the proximal gradient algorithm with extrapolation for minimizing the sum of a Lipschitz differentiable function and a proper closed convex function. Under the error bound condition used in [Ann. Oper. Res., 46 (1993), pp. 157-178] for analyzing the convergence of the proximal gradient algorithm, we show that there exists a threshold such that if the extrapolation coefficients are chosen below this threshold, then the sequence generated converges R-linearly to a stationary point of the problem. Moreover, the corresponding sequence of objective values is also R-linearly convergent. In addition, the threshold reduces to 1 for convex problems, and as a consequence we obtain the R-linear convergence of the sequence generated by FISTA with fixed restart. Finally, we present some numerical experiments to illustrate our results. | Keywords: | Linear convergence Extrapolation Error bound Accelerated gradient method Nonconvex nonsmooth minimization Convex minimization |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on optimization | ISSN: | 1052-6234 | EISSN: | 1095-7189 | DOI: | 10.1137/16M1055323 | Rights: | © 2017 Society for Industrial and Applied Mathematics The following publication Wen, B., Chen, X., & Pong, T. K. (2017). Linear convergence of proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth minimization problems. SIAM Journal on Optimization, 27(1), 124-145 is available at https://doi.org/10.1137/16M1055323 |
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