Critical point concepts: a fixed-point approach

Abdellatif Moudafi (1, 2)

1 LSIS - Laboratoire des Sciences de l'Information et des Systèmes
2 I&M - Images et Modèles

Inspired by the notion of critical points for DC functions and given two mappings P and Q, we introduce the concept of critical points in the fixed-point context and design and algorithm for finding such points. Connections are then made with the DC optimization case. We show that the proposed Algorithmic approach coincides with the celebrate DCA introduced by Pham Dinh Tao. The case of maximal monotone operators is also stated and investigated via a characterization of their associated resolvents.

Mots clés: critical point; fixed-point problem; DC optimization; DCA; proximity; resolvent; convex function; conjugate function; monotone operators; duality

Domaines: Traitement du signal et de l'image [eess.SP]

Abdellatif Moudafi. Critical point concepts: a fixed-point approach. 2022. ⟨hal-01479327⟩