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http://hdl.handle.net/10397/106616
Title: | An inexact regularized proximal Newton method for nonconvex and nonsmooth optimization | Authors: | Liu, R Pan, S Wu, Y Yang, X |
Issue Date: | Jun-2024 | Source: | Computational optimization and applications, June 2024, v. 88, no. 2, p. 603-641 | Abstract: | This paper focuses on the minimization of a sum of a twice continuously differentiable function f and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of f involving the th power of the KKT residual. For = 0, we justify the global convergence of the iterate sequence for the KL objective function and its R-linear convergence rate for the KL objective function of exponent 1/2. For ∈ (0,1), by assuming that cluster points satisfy a locally Hölderian error bound of order q on a second-order stationary point set and a local error bound of order q > 1+ on the common stationary point set, respectively, we establish the global convergence of the iterate sequence and its superlinear convergence rate with order depending on q and . A dual semismooth Newton augmented Lagrangian method is also developed for seeking an inexact minimizer of subproblems. Numerical comparisons with two state-of-the-art methods on 1-regularized Student’s t-regressions, group penalized Student’s t-regressions, and nonconvex image restoration confirm the efficiency of the proposed method. | Keywords: | Convergence rate Global convergence KL function Metric q-subregularity Nonconvex and nonsmooth optimization Regularized proximal Newton method |
Publisher: | Springer New York LLC | Journal: | Computational optimization and applications | ISSN: | 0926-6003 | EISSN: | 1573-2894 | DOI: | 10.1007/s10589-024-00560-0 | Rights: | © The Author(s) 2024 This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The following publication Liu, R., Pan, S., Wu, Y. et al. An inexact regularized proximal Newton method for nonconvex and nonsmooth optimization. Comput Optim Appl 88, 603–641 (2024) is available at https://doi.org/10.1007/s10589-024-00560-0. |
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