An adaptive regularization method in Banach spaces

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Résumé

This paper considers optimization of nonconvex functionals in smooth infinite dimensional spaces. It is first proved that functionals in a class containing multivariate polynomials augmented with a sufficiently smooth regularization can be minimized by a simple linesearch-based algorithm. Sufficient smoothness depends on gradients satisfying a novel two-terms generalized Lipschitz condition. A first-order adaptive regularization method applicable to functionals with β-Hölder continuous derivatives is then proposed, that uses the linesearch approach to compute a suitable trial step. It is shown to find an ϵ-approximate first-order point in at most (Formula presented.) evaluations of the functional and its first p derivatives.

langue originaleAnglais
Pages (de - à)1163-1179
Nombre de pages17
journalOptimization Methods and Software
Volume38
Numéro de publication6
Les DOIs
Etat de la publicationPublié - 24 nov. 2023

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