Year: 2023
Author: Ziang Chen, Andre Milzarek, Zaiwen Wen
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 683–716
Abstract
We propose a trust-region type method for a class of nonsmooth nonconvex optimization problems where the objective function is a summation of a (probably nonconvex) smooth function and a (probably nonsmooth) convex function. The model function of our trust-region subproblem is always quadratic and the linear term of the model is generated using abstract descent directions. Therefore, the trust-region subproblems can be easily constructed as well as efficiently solved by cheap and standard methods. When the accuracy of the model function at the solution of the subproblem is not sufficient, we add a safeguard on the stepsizes for improving the accuracy. For a class of functions that can be "truncated'', an additional truncation step is defined and a stepsize modification strategy is designed. The overall scheme converges globally and we establish fast local convergence under suitable assumptions. In particular, using a connection with a smooth Riemannian trust-region method, we prove local quadratic convergence for partly smooth functions under a strict complementary condition. Preliminary numerical results on a family of $\ell_1$-optimization problems are reported and demonstrate the efficiency of our approach.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2110-m2020-0317
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 683–716
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Trust-region method Nonsmooth composite programs Quadratic model function Global and local convergence.
Author Details
-
Proximal gradient algorithm with trust region scheme on Riemannian manifold
Zhao, Shimin
Yan, Tao
Zhu, Yuanguo
Journal of Global Optimization, Vol. 88 (2024), Iss. 4 P.1051
https://doi.org/10.1007/s10898-023-01326-4 [Citations: 0]