Fully Adaptive Zeroth-Order Method for Minimizing Functions with Compressible Gradients

Geovani N. Grapiglia () and Daniel McKenzie ()
Additional contact information
Geovani N. Grapiglia: Université catholique de Louvain
Daniel McKenzie: Colorado School of Mines

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 33, 25 pages

Abstract: Abstract We propose an adaptive zeroth-order method for minimizing differentiable functions with L-Lipschitz continuous gradients. The method is designed to take advantage of the eventual compressibility of the gradient of the objective function, but it does not require knowledge of the approximate sparsity level s or the Lipschitz constant L of the gradient. We show that the new method performs no more than $$\mathcal {O}\left( n^{2}\epsilon ^{-2}\right) $$ O n 2 ϵ - 2 function evaluations to find an $$\epsilon $$ ϵ -approximate stationary point of an objective function with n variables. Assuming additionally that the gradients of the objective function are compressible, we obtain an improved complexity bound of $$\mathcal {O}\left( s\log \left( n\right) \epsilon ^{-2}\right) $$ O s log n ϵ - 2 function evaluations, which holds with high probability. Preliminary numerical results illustrate the efficiency of the proposed method and demonstrate that it can significantly outperform its non-adaptive counterpart.

Keywords: Derivative-free optimization; Black-box optimization; Zeroth-order optimization; Worst-case complexity; Compressible gradients (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02860-9 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:joptap:v:208:y:2026:i:1:d:10.1007_s10957-025-02860-9

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02860-9

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

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