Global and local R-linear convergence of a spectral projected gradient method for convex optimization with singular solution
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Authors
Zhensheng Yu
- College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, P. R. China.
Xinyue Gan
- College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, P. R. China.
Abstract
In this paper, we propose a spectral projected gradient method for the convex optimization problem
with singular solution. By solving the equivalent equation of the gradient function, this method combines
the perturbed spectral gradient direction with the projection direction to generate the next iteration point.
Under some mild conditions, we establish the global convergence and the local R-linear convergence rate
under the local error bound condition. Preliminary numerical tests are given to show that the proposed
method works well.
Share and Cite
ISRP Style
Zhensheng Yu, Xinyue Gan, Global and local R-linear convergence of a spectral projected gradient method for convex optimization with singular solution, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4509--4519
AMA Style
Yu Zhensheng, Gan Xinyue, Global and local R-linear convergence of a spectral projected gradient method for convex optimization with singular solution. J. Nonlinear Sci. Appl. (2016); 9(6):4509--4519
Chicago/Turabian Style
Yu, Zhensheng, Gan, Xinyue. "Global and local R-linear convergence of a spectral projected gradient method for convex optimization with singular solution." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4509--4519
Keywords
- Unconstrained optimization
- spectral projected gradient
- local error bound
- R-linear convergence.
MSC
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