Stability of metric regularity with set-valued perturbations and application to Newton’s method for solving generalized equations

Samir Adly (1) , Huynh Van Ngai (1) , Nguyen Van Vu (1)

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information

In this paper, we deal firstly with the question of the stability of the metric regularity under set-valued perturbation. By adopting the measure of closeness between two multifunctions, we establish some stability results on the semi-local/local metric regularity. These results are applied to study the convergence of iterative schemes of Newton-type methods for solving generalized equations in which the set-valued part is approximated. Some examples illustrating the applicability of the proposed method are discussed.

Mots clés: Generalized equation; Metric regularity; Newton’s method; Linear/superlinear convergence

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Samir Adly, Huynh Van Ngai, Nguyen Van Vu. Stability of metric regularity with set-valued perturbations and application to Newton’s method for solving generalized equations. Set-Valued and Variational Analysis, 2017, 25 (3), pp.543-567. ⟨10.1007/s11228-017-0438-3⟩. ⟨hal-01613819⟩