@article{701f14f47e074266a4eb86718c0f8939,
title = "Adaptive regularization for nonconvex optimization using inexact function values and randomly perturbed derivatives",
abstract = "A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function with Lipschitz continuous p-th derivative and given an arbitrary optimality order q≤p, an upper bound on the number of function and derivatives evaluations is established for this algorithm. This bound is in expectation, and in terms of a power of the required tolerances, this power depending on whether q≤2 or q>2. Moreover these bounds are sharp in the order of the accuracy tolerances. An extension to convexly constrained problems is also outlined.",
keywords = "Evaluation complexity, Inexact functions and derivatives, Regularization methods, Stochastic analysis",
author = "S. Bellavia and G. Gurioli and B. Morini and Toint, {Ph L.}",
note = "Funding Information: INdAM-GNCS partially supported the first, second and third authors under Progetti di Ricerca 2019, Project “Tecniche adattive per metodi di ottimizzazione in Machine Learning”. The last author gratefully acknowledges the support and friendly environment provided by the Department of Industrial Engineering at the Universit{\`a} degli Studi di Firenze (Italy), grant “Bando Professori visitatori 2020”, during his visit in the fall of 2020. Funding Information: INdAM-GNCS partially supported the first, second and third authors under Progetti di Ricerca 2019, Project ?Tecniche adattive per metodi di ottimizzazione in Machine Learning?. The last author gratefully acknowledges the support and friendly environment provided by the Department of Industrial Engineering at the Universit? degli Studi di Firenze (Italy), grant ?Bando Professori visitatori 2020?, during his visit in the fall of 2020. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2022",
month = feb,
doi = "10.1016/j.jco.2021.101591",
language = "English",
volume = "68",
journal = "Journal of Complexity",
issn = "0885-064X",
publisher = "Academic Press Inc.",
}