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.

On the constrained minimization of smooth Kurdyka– Lojasiewicz functions with the scaled gradient projection method / Prato, Marco; Bonettini, Silvia; Loris, Ignace; Porta, Federica; Rebegoldi, Simone. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - STAMPA. - 756:(2016), pp. 1-6. ((Intervento presentato al convegno 6th International Workshop on New Computational Methods for Inverse Problems tenutosi a Cachan nel 20 maggio 2016 [10.1088/1742-6596/756/1/012001].

### On the constrained minimization of smooth Kurdyka– Lojasiewicz functions with the scaled gradient projection method

#### Abstract

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.
##### Scheda breve Scheda completa Scheda completa (DC)
2016
6th International Workshop on New Computational Methods for Inverse Problems
Cachan
20 maggio 2016
756
1
6
Prato, Marco; Bonettini, Silvia; Loris, Ignace; Porta, Federica; Rebegoldi, Simone
On the constrained minimization of smooth Kurdyka– Lojasiewicz functions with the scaled gradient projection method / Prato, Marco; Bonettini, Silvia; Loris, Ignace; Porta, Federica; Rebegoldi, Simone. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - STAMPA. - 756:(2016), pp. 1-6. ((Intervento presentato al convegno 6th International Workshop on New Computational Methods for Inverse Problems tenutosi a Cachan nel 20 maggio 2016 [10.1088/1742-6596/756/1/012001].
File in questo prodotto:
File
JPCS_756_1_012001.pdf

Open access

Tipologia: Versione pubblicata dall'editore
Dimensione 716.39 kB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/1100005`