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Pré-Publication, Document De Travail Année : 2022

Harnessing structure in composite nonsmooth minimization

Gilles Bareilles
Franck Iutzeler
Jérôme Malick

Résumé

We consider the problem of minimizing the composition of a nonsmooth function with a smooth mapping in the case where the proximity operator of the nonsmooth function can be explicitly computed. We first show that this proximity operator can provide the exact smooth substructure of minimizers, not only of the nonsmooth function, but also of the full composite function. We then exploit this proximal identification by proposing an algorithm which combines proximal steps with sequential quadratic programming steps. We show that our method locally identifies the optimal smooth substructure and then converges quadratically. We illustrate its behavior on two problems: the minimization of a maximum of quadratic functions and the minimization of the maximal eigenvalue of a parametrized matrix.
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Dates et versions

hal-03706958 , version 1 (28-06-2022)
hal-03706958 , version 2 (09-02-2023)
hal-03706958 , version 3 (20-03-2023)

Identifiants

  • HAL Id : hal-03706958 , version 2

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Gilles Bareilles, Franck Iutzeler, Jérôme Malick. Harnessing structure in composite nonsmooth minimization. 2022. ⟨hal-03706958v2⟩
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