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-Łojasiewicz property at each point of its domain and its gradient is Lipschitz continuous.
Highlights
=:y(k) where αk is a scalar steplength parameter, Dk is a symmetric positive definite matrix and PΩ,Dk−1(·) is the projection onto Ω associated to the norm induced by Dk−1 [4]
The scaled gradient projection (SGP) method is a variable metric forward-backward algorithm [11, 12] which has been exploited in the last years for the solution of different real-world inverse problems [5, 6, 7, 16, 17, 18]
The main difference between SGP and the standard forward-backward schemes is the presence of two independent parameters αk and λk with a complete different role: while the last one is automatically computed with the Armijo condition (2) to guarantee the sufficient decrease of the objective function, the first one can be chosen to improve the actual convergence rate of the method, exploiting thirty years of literature in numerical optimization [3, 13, 19, 20]
Summary
This content has been downloaded from IOPscience. Please scroll down to see the full text. Ser. 756 012001 (http://iopscience.iop.org/1742-6596/756/1/012001) View the table of contents for this issue, or go to the journal homepage for more. Download details: IP Address: 155.185.102.48 This content was downloaded on 02/11/2016 at 15:13. Please note that terms and conditions apply. You may be interested in: An image reconstruction method from Fourier data with uncertainties on the spatial frequencies Anastasia Cornelio, Silvia Bonettini and Marco Prato Stochastic variational approach to minimum uncertainty states F Illuminati and L Viola Interactions between polyelectrolyte-macroion complexes H. R. Netz Design of copolymeric materials T Kurosky and J M Deutsch On the linear statistics of Hermitian random matrices Yang Chen and Nigel Lawrence Theoretical description of the nucleation of vapor bubbles in a superheated fluid J. Lutsko Numerical identifications of parameters in parabolic systems Yee Lo Keung and Jun Zou
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