A proximal bundle approach for solving the generalized variational inequalities with inexact data

Ming Huang, Si Qi Zhang, Yong Xiu Feng, Jin Long Yuan and Hong Han Bei

Applied Mathematics and Computation, 2025, vol. 491, issue C

Abstract: This paper introduces a proximal bundle scheme to solve generalized variational inequalities with inexact data. Under optimality conditions, the problem can be equivalently represented as seeking out the zero point of the sum of two multi-valued operators whose domains are the real Hilbert space. The two operators denoted by T and f, respectively, are the monotone operator and the subdifferential of a lower semi-continuous, non-differentiable, convex function. Our approach is based on the principles of the proximal point strategy, which involves incorporating inexact information into the subproblems and approximating them using a series of piecewise linear convex functions. Moreover, we put forward a novel stopping criterion to identify the adequacy of the current approximation. This approach serves to make the subproblems more manageable, and it has been proven that obtaining inexact information can ensure that the linearization error during the iteration process remains non-negative, thus avoiding triggering noise attenuation. Subsequently, we verify the convergence of the algorithm under relatively mild assumptions (the operator T is para-monotone and may be multi-valued). Ultimately, we present the findings of elementary numerical experiments to declare the method's efficacy.

Keywords: Convex optimization; Nonsmooth optimization; Inexact information; Generalized variational inequalities; Proximal bundle method (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324005484
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:491:y:2025:i:c:s0096300324005484

DOI: 10.1016/j.amc.2024.129087

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().