On the constrained minimization of smooth Kurdyka—?ojasiewicz functions with the scaled gradient projection method

6th International Workshop on New Computational Methods for Inverse Problems

物理学;计算机科学

Prato, Marco^1 ; Bonettini, Silvia^2 ; Loris, Ignace^3 ; Porta, Federica^2 ; Rebegoldi, Simone^1

Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via Campi 213/b, Modena

41125, Italy^1

Dipartimento di Matematieca e Informatica, Università di Ferrara, Via Saragat 1, Ferrara

44122, Italy^2

Département de Mathematique, Université Libre de Bruxelles, Boulevard du Triomphe, Bruxelles

1050, Belgium^3

关键词: Constrained minimization;    Convergence results;    First order optimization method;    Gradient projection methods;    Gradient projections;    Lipschitz continuous;    Nonconvex functions;    Objective functions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/756/1/012001/pdf
DOI  :  10.1088/1742-6596/756/1/012001

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

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.