Full-low evaluation methods for bound and linearly constrained derivative-free optimization

C. W. Royer (), O. Sohab () and L. N. Vicente ()
Additional contact information
C. W. Royer: Université Paris Dauphine-PSL, Place du Maréchal de Lattre de Tassigny
O. Sohab: Lehigh University
L. N. Vicente: Lehigh University

Computational Optimization and Applications, 2024, vol. 89, issue 2, No 1, 279-315

Abstract: Abstract Derivative-free optimization (DFO) consists in finding the best value of an objective function without relying on derivatives. To tackle such problems, one may build approximate derivatives, using for instance finite-difference estimates. One may also design algorithmic strategies that perform space exploration and seek improvement over the current point. The first type of strategy often provides good performance on smooth problems but at the expense of more function evaluations. The second type is cheaper and typically handles non-smoothness or noise in the objective better. Recently, full-low evaluation methods have been proposed as a hybrid class of DFO algorithms that combine both strategies, respectively denoted as Full-Eval and Low-Eval. In the unconstrained case, these methods showed promising numerical performance. In this paper, we extend the full-low evaluation framework to bound and linearly constrained derivative-free optimization. We derive convergence results for an instance of this framework, that combines finite-difference quasi-Newton steps with probabilistic direct-search steps. The former are projected onto the feasible set, while the latter are defined within tangent cones identified by nearby active constraints. We illustrate the practical performance of our instance on standard linearly constrained problems, that we adapt to introduce noisy evaluations as well as non-smoothness. In all cases, our method performs favorably compared to algorithms that rely solely on Full-eval or Low-eval iterations.

Keywords: Derivative-free optimization; Bound constraints; Linear constraints; Feasible methods (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-024-00596-2 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:coopap:v:89:y:2024:i:2:d:10.1007_s10589-024-00596-2

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

DOI: 10.1007/s10589-024-00596-2

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 ().