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On the constrained minimization of smooth Kurdyka-Łojasiewicz functions with the scaled gradient projection method

par Prato, Marco;Bonettini, Silvia;Loris, Ignace ;Porta, Federica;Rebegoldi, Simone
Référence Journal of physics. Conference series, 756, 1, 012001
Publication Publié, 2016

Article révisé par les pairs

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Résumé :

The scaled gradient projection (SGP) method is a first-order optimization method applicable to the constrained minimization of smooth functions and exploiting a scaling matrix multiplying the gradient and a variable steplength parameter to improve the convergence of the scheme. For a general nonconvex function, the limit points of the sequence generated by SGP have been proved to be stationary, while in the convex case and with some restrictions on the choice of the scaling matrix the sequence itself converges to a constrained minimum point. In this paper we extend these convergence results by showing that the SGP sequence converges to a limit point provided that the objective function satisfies the Kurdyka-Lojasiewicz property at each point of its domain and its gradient is Lipschitz continuous.