Quadratic regularization methods with finite-difference gradient approximations

Geovani Nunes Grapiglia ()
Additional contact information
Geovani Nunes Grapiglia: Université catholique de Louvain, ICTEAM/INMA

Computational Optimization and Applications, 2023, vol. 85, issue 3, No 2, 683-703

Abstract: Abstract This paper presents two quadratic regularization methods with finite-difference gradient approximations for smooth unconstrained optimization problems. One method is based on forward finite-difference gradients, while the other is based on central finite-difference gradients. In both methods, the accuracy of the gradient approximations and the regularization parameter in the quadratic models are jointly adjusted using a nonmonotone acceptance condition for the trial points. When the objective function is bounded from below and has Lipschitz continuous gradient, it is shown that the method based on forward finite-difference gradients needs at most $${\mathcal{O}}\left( n\epsilon ^{-2}\right) $$ O n ϵ - 2 function evaluations to generate a $$\epsilon $$ ϵ -approximate stationary point, where n is the problem dimension. Under the additional assumption that the Hessian of the objective is Lipschitz continuous, an evaluation complexity bound of the same order is proved for the method based on central finite-difference gradients. Numerical results are also presented. They confirm the theoretical findings and illustrate the relative efficiency of the proposed methods.

Keywords: Nonconvex Optimization; Derivative-Free Methods; Finite-Differences; Worst-Case Complexity (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-022-00373-z 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:coopap:v:85:y:2023:i:3:d:10.1007_s10589-022-00373-z

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-022-00373-z

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

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