Éditeur(s) : HAL CCSD Heldermann
Résumé : International audience
Journal of Convex Analysis

hal-00507803
https://hal.archives-ouvertes.fr/hal-00507803

Éditeur(s) : HAL CCSD Heldermann
Résumé : International audience
We study extended notions for sums of monotone operators and for precompositions of monotone operators with continuous linear mappings. First, we establish some new properties related to the notion of extended sum recently proposed by Revalski and Théra, among them the monotonicity of this sum provided the operators involved are maximal monotone. Then, we show that the equivalence which exists between usual sums and compositions remains valid also for the extended operations. This allows us to obtain some known and new results for extended compositions via the corresponding properties of extended sums.
Journal of Convex Analysis

hal-00698807
https://hal.archives-ouvertes.fr/hal-00698807

Éditeur(s) : HAL CCSD Heldermann
Résumé : International audience
Let f : X → R ∪ {+∞} be a lower semicontinuous function on a Banach space X. We show that f is quasiconvex if and only if its Clarke subdifferential ∂f is quasimonotone. As an immediate consequence, we get that f is convex if and only if ∂f is monotone.
Journal of Convex Analysis

hal-00699221
https://hal.archives-ouvertes.fr/hal-00699221

Éditeur(s) : HAL CCSD Heldermann
Résumé : International audience
We present an iterative method for finding zeroes of maximal monotone operators in a real Hilbert space. The underlying idea relies upon the discretization of a first order dissipative dynamical system which allows us to preserve the local feature, as well as to obtain convergence results. The main theorems do not only recover known convergence results of standard and inertial proximal methods, but also provide a theoretical basis for the application of new iterative methods.
Journal of Convex Analysis

hal-00780210
https://hal.univ-antilles.fr/hal-00780210