A dynamic gradient approach to Pareto optimization with nonsmooth nonconvex objective functions
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 dierentiable objective functions. Based on the Yosida regularization of the subdierential 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; subdierential 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
Entry Submitted: 06/06/2014
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