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- W4379880189 abstract "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." @default.
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- W4379880189 date "2023-06-08" @default.
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- W4379880189 title "An adaptive regularization method in Banach spaces" @default.
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- W4379880189 doi "https://doi.org/10.1080/10556788.2023.2210253" @default.
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