244 research outputs found
A dynamic gradient approach to Pareto optimization with nonsmooth convex objective functions
In a general Hilbert framework, we consider continuous gradient-like
dynamical systems for constrained multiobjective optimization involving
non-smooth convex objective functions. Our approach is in the line of a
previous work where was considered the case of convex di erentiable objective
functions. Based on the Yosida regularization of the subdi erential operators
involved in the system, we obtain the existence of strong global trajectories.
We prove a descent property for each objective function, and the convergence of
trajectories to weak Pareto minima. This approach provides a dynamical
endogenous weighting of the objective functions. Applications are given to
cooperative games, inverse problems, and numerical multiobjective optimization
Radial solutions of Lane-Emden-Fowler equations with Pucci's extremal operators
We report on some recent results obtained for positive radial solutions of Lane-Emden-Fowler type equations with Pucci's operators as principal parts. The presented results include the asymptotic analysis of almost critical solutions in the unit ball, existence results in annular domains and sharp Liouville-type results for exterior Dirichlet problems.
- …