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A dynamic gradient approach to Pareto optimization with nonsmooth nonconvex objective functions

Hédy Attouch(hedy.attouch***at***univ-montp2.fr)
Guillaume Garrigos(guillaume.garrigos***at***gmail.com)
Xavier Goudou(xavier.goudou***at***yahoo.fr)

Abstract: 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.

Keywords: multiobjective optimization; continuous gradient systems; convex objective functions; subdi erential operators; asymptotic behavior; Pareto critical; Pareto optimization; forwardbackward methods; sparse optimization; signal/imaging processing.

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Convex and Nonsmooth Optimization

Citation:

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Entry Submitted: 06/06/2014
Entry Accepted: 06/06/2014
Entry Last Modified: 06/06/2014

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