Asymptotic behavior of dynamical system governed by monotone operators and applications

Abstract

To solve inclusion governed by maximal monotone operator, we consider the associated Cauchy problem with a parameter in Yosida approximate that depends on time. This allows us to generate trajectories that converge weakly, as t tends to infinity, to the solution of the inclusion problem. No additional assumptions are required for the operator. As a main application, we consider the non-autonomous continuous dynamical systems which are linked to Newton and Levenberg–Marquardt methods. The second application concerns the convex structured minimisation problems.