An adaptive regularization method in Banach spaces

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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.

Original languageEnglish
Pages (from-to)1163-1179
Number of pages17
JournalOptimization Methods and Software
Issue number6
Publication statusPublished - 24 Nov 2023


  • adaptive regularization
  • evaluation complexity
  • Hölder gradients
  • infinite-dimensional problems
  • Nonlinear optimization


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    Philippe Toint (Visiting researcher)

    21 Nov 20212 Dec 2021

    Activity: Visiting an external institution typesVisiting an external academic institution

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