Results 91 to 100 of about 257,170 (166)

Subdifferential characterization of approximate convexity: the lower semicontinuous case

, 2009
International audienceIt is known that a locally Lipschitz function f is approximately convex if, and only if, its Clarke subdifferential ∂C f is a submonotone operator. The main object of this work is to extend the above characterization to the class of
Lassonde, Marc, Daniilidis, Aris, Jules, Florence   +2 more
core   +1 more source

Dirichlet μ-Parametric Differential Problem with Multivalued Reaction Term

Mathematics
We study a Dirichlet μ-parametric differential problem driven by a variable competing exponent operator, given by the sum of a negative p-Laplace differential operator and a positive q-Laplace differential operator, with a multivalued reaction term in ...
Mina Ghasemi, Calogero Vetro, Zhenfeng Zhang   +2 more
doaj   +1 more source

The effects of Clarke sub-differential and Poisson jumps on nonlocal controllability of Sobolev-type fractional stochastic differential inclusions

Journal of Inequalities and Applications
This paper explores Sobolev-type Atangana–Baleanu fractional stochastic differential inclusions driven by fractional Brownian motion, incorporating Clarke sub-differentials, Poisson jumps, and nonlocal conditions.
Wael W. Mohammed, Hamdy M. Ahmed, Homan Emadifar, Karim K. Ahmed, A. M. Sayed Ahmed   +4 more
doaj   +1 more source

Lipschitz Functions with Maximal Clarke Subdifferentials Are Generic

, 1998
. We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point.
Jonathan M. Borwein, Xianfu Wang
core  

Critical metrics of eigenvalue functionals via Clarke subdifferential

62 ...
Petrides, Romain, Tewodrose, David
openaire   +2 more sources

Topological Properties of the Approximate Subdifferential

, 1994
The approximate subdifferential introduced by Mordukhovich has attracted much attention in recent works on nonsmooth optimization. Potential advantages over other concepts of subdifferentiability might be related to its non-convexity.
René Henrion
core  

Pseudomonotone diagonal subdifferential operators

, 2013
Let f be an equilibrium bifunction defined on the product space X x X, where X is a Banach space. If f is locally Lipschitz with respect to the second variable, for every x in X we define T_f(x) as the Clarke subdifferential of f(x,\\cdot) evaluated at x.
GIULI, MASSIMILIANO, CASTELLANI, MARCO
core  

Some notes on weak subdifferential

, 2017
Some necessary conditions for having nonempty weak subdifferential of a function are presented and the positively homogeneous of the weak subdifferential operator is proved. Necessary and sufficient conditions for achieving a global minimum of a
Ali Farajzadeh, P. Cheraghi, Gradimir Milovanovic   +2 more
core   +1 more source

Subdifferential Test for Optimality

, 2013
International audienceWe provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach spaces using the concept of subdifferential.
Lassonde, Marc, Jules, Florence
core   +1 more source

On invex functions with same η in single and multivalued nonsmooth optimization with Clarke's subdifferential

In this paper, a finite family of nonsmooth locally Lipschitz continuous functions that are invex with respect to the same function η are characterized in terms of their scalarized counterparts.
Rinne, Ville, Nikulin, Yury, Mäkelä, Marko   +2 more
openaire   +2 more sources