A multi-step inertial extragradient algorithm for nonsmooth and nonconvex composite optimization problems

Zhixue Wang () and Hongjin He ()
Additional contact information
Zhixue Wang: Ningbo University
Hongjin He: Ningbo University

Journal of Global Optimization, 2025, vol. 93, issue 2, No 6, 489-521

Abstract: Abstract We are concerned with minimizing a composite objective function, which can be decomposed into a differentiable but not necessarily convex part and a convex but possibly nonsmooth function. To efficiently exploit the decomposable structure, in this paper, we propose a Multi-step inertial ExtraGradient Algorithm (MEGA), which consists of two inertial steps involving the combination of finite historical iterates and two proximal gradient steps evaluating the proximal operators of a convex function at some points. With the help of Kurdyka-Łojasiewicz property, we theoretically prove that the sequence generated by our MEGA is globally convergent to a stationary point of the problem under consideration. A series of numerical experiments on Lasso and nonconvex quadratic optimization problems show that the proposed MEGA works well in practice. Particularly exciting is the illustration by some computational results that our MEGA can escape local minima points (at least with high probability) to reach a global solution. This strongly supports the idea that utilizing more historical information in extragradient methods is beneficial for solving nonconvex optimization problems.

Keywords: Extragradient method; Composite optimization; Nonsmooth nonconvex optimization; Kurdyka-Łojasiewicz inequality; Proximal gradient method; 90C26; 90C90 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-025-01532-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:93:y:2025:i:2:d:10.1007_s10898-025-01532-2

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-025-01532-2

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().