A multi-precision quadratic regularization method for unconstrained optimization with rounding error analysis

Dominique Monnet () and Dominique Orban ()
Additional contact information
Dominique Monnet: Université de Rennes
Dominique Orban: HEC Montréal

Computational Optimization and Applications, 2025, vol. 91, issue 3, No 1, 997-1031

Abstract: Abstract We propose a multi-precision extension of the Quadratic Regularization (R2) algorithm that enables it to take advantage of low-precision computations, and by extension to decrease energy consumption during the solve. The lower the precision in which computations occur, the larger the errors induced in the objective value and gradient, as well as in all other computations that occur in the course of the iterations. The Multi-Precision R2 (MPR2) algorithm monitors the accumulation of rounding errors with two aims: to provide guarantees on the result of all computations, and to permit evaluations of the objective and its gradient in the lowest precision possible while preserving convergence properties. MPR2’s numerical results show that single precision offers enough accuracy for more than half of objective evaluations and most of gradient evaluations during the algorithm’s execution. However, MPR2 fails to converge on several problems of the test set for which double precision does not offer enough precision to ensure the convergence conditions before reaching a first order critical point. That is why we propose a practical version of MPR2 with relaxed conditions which converges for almost as many problems as R2 and potentially enables saving about 50% time and 60% energy for objective evaluation and 50% time and 70% energy for gradient evaluation.

Keywords: Unconstrained optimization; Quadratic regularization; Multi precision; Rounding error analysis (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-025-00676-x 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:91:y:2025:i:3:d:10.1007_s10589-025-00676-x

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

DOI: 10.1007/s10589-025-00676-x

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 ().