A dynamic gradient approach to Pareto optimization with nonsmooth convex objective functions |
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Authors: | Hé dy Attouch,Guillaume Garrigos,Xavier Goudou |
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Affiliation: | Institut de Mathématiques et Modélisation de Montpellier, UMR 5149 CNRS, Université Montpellier 2, place Eugène Bataillon, 34095 Montpellier cedex 5, France |
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Abstract: | In a general Hilbert framework, we consider continuous gradient-like dynamical systems for constrained multiobjective optimization involving nonsmooth convex objective functions. Based on the Yosida regularization of the subdifferential 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, a key property for applications in cooperative games, inverse problems, and numerical multiobjective optimization. |
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Keywords: | Multiobjective convex optimization Pareto optima Multiobjective steepest descent Subdifferential operators Asymptotic behavior Gradient-like methods |
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