A double-projection-based algorithm for large-scale nonlinear systems of monotone equations

2014 ◽  
Vol 68 (2) ◽  
pp. 213-228 ◽  
Author(s):  
Keyvan Amini ◽  
Ahmad Kamandi ◽  
Somayeh Bahrami
Keyword(s):  
Nonlinear Systems ◽  
Large Scale ◽  
Monotone Equations

scholarly journals An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Gaohang Yu ◽  
Shanzhou Niu ◽  
Jianhua Ma ◽  
Yisheng Song
Keyword(s):  
Nonlinear Systems ◽  
Large Scale ◽  
Signal Reconstruction ◽  
Correction Method ◽  
Merit Function ◽  
Convergence Result ◽  
Image Deconvolution ◽  
Practical Applications ◽  
Monotone Equations ◽  
Adaptive Prediction

Combining multivariate spectral gradient method with projection scheme, this paper presents an adaptive prediction-correction method for solving large-scale nonlinear systems of monotone equations. The proposed method possesses some favorable properties: (1) it is progressive step by step, that is, the distance between iterates and the solution set is decreasing monotonically; (2) global convergence result is independent of the merit function and its Lipschitz continuity; (3) it is a derivative-free method and could be applied for solving large-scale nonsmooth equations due to its lower storage requirement. Preliminary numerical results show that the proposed method is very effective. Some practical applications of the proposed method are demonstrated and tested on sparse signal reconstruction, compressed sensing, and image deconvolution problems.

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