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Article Dans Une Revue Optimization Methods and Software Année : 2023

An adaptive regularization method in Banach spaces

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 O(ϵ−p+βp+β−1) evaluations of the functional and its first p derivatives.
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Dates et versions

hal-04436386 , version 1 (03-02-2024)

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Serge Gratton, Sadok Jerad, Philippe L. Toint. An adaptive regularization method in Banach spaces. Optimization Methods and Software, 2023, 38 (6), pp.1163-1179. ⟨10.1080/10556788.2023.2210253⟩. ⟨hal-04436386⟩
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