Name
Title | ||
|---|---|---|
Linear Convergence of Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems |
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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/16M1055323 | SIAM JOURNAL ON OPTIMIZATION |
Keywords | Field | DocType |
linear convergence,extrapolation,error bound,accelerated gradient method,nonconvex nonsmooth minimization,convex minimization | Convergence (routing),Algorithm,Differentiable function,Stationary point,Extrapolation,Closed convex function,Rate of convergence,Lipschitz continuity,Convex optimization,Mathematics | Journal |
Volume | Issue | ISSN |
27 | 1 | 1052-6234 |
Citations | PageRank | References |
14 | 0.58 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bo Wen | 1 | 18 | 1.99 |
| Xiaojun Chen | 2 | 1298 | 107.51 |
| Ting Kei Pong | 3 | 427 | 23.18 |