scholarly journals An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration

2021 ◽  
Vol 6 (1) ◽  
pp. 235-260 ◽  
Author(s):  
Abdulkarim Hassan Ibrahim ◽  
◽  
Poom Kumam ◽  
Auwal Bala Abubakar ◽  
Umar Batsari Yusuf ◽  
...  
Keyword(s):  
Image Restoration ◽  
Nonlinear Equations ◽  
Projection Algorithm ◽  
Constrained Nonlinear Equations

scholarly journals A Nonmonotone Projection Method for Constrained System of Nonlinear Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Yazheng Dang ◽  
Wenwen Liu
Keyword(s):  
Numerical Experiment ◽  
Nonlinear Equations ◽  
Suitable Condition ◽  
Projection Algorithm ◽  
Iterative Sequence ◽  
System Of Nonlinear Equations ◽  
Projection Algorithms ◽  
Constrained System ◽  
Slow Convergence ◽  
Constrained Nonlinear Equations

This paper deals with the nonmonotone projection algorithm for constrained nonlinear equations. For some starting points, the previous projection algorithms for the problem may encounter slow convergence which is related to the monotone behavior of the iterative sequence as well as the iterative direction. To circumvent this situation, we adopt the nonmonotone technique introduced by Dang to develop a nonmonotone projection algorithm. After constructing the nonmonotone projection algorithm, we show its convergence under some suitable condition. Preliminary numerical experiment is reported at the end of this paper, from which we can see that the algorithm we propose converges more quickly than that of the usual projection algorithm for some starting points.

scholarly journals Derivative-free HS-DY-type method for solving nonlinear equations and image restoration

Heliyon ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. e05400
Author(s):  
Auwal Bala Abubakar ◽  
Poom Kumam ◽  
Abdulkarim Hassan Ibrahim ◽  
Jewaidu Rilwan
Keyword(s):  
Image Restoration ◽  
Nonlinear Equations ◽  
Type Method ◽  
Derivative Free

scholarly journals Solving Adaptive Image Restoration Problems via a Modified Projection Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Hao Yang ◽  
Xueping Luo ◽  
Leiting Chen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Image Restoration ◽  
Image Denoising ◽  
Existence And Uniqueness ◽  
Experimental Results ◽  
Projection Algorithm ◽  
Tv Regularization ◽  
Uniqueness Of The Solution ◽  
Quasi Variational Inequality

We introduce a new general TV regularizer, namely, generalized TV regularization, to study image denoising and nonblind image deblurring problems. In order to discuss the generalized TV image restoration with solution-driven adaptivity, we consider the existence and uniqueness of the solution for mixed quasi-variational inequality. Moreover, the convergence of a modified projection algorithm for solving mixed quasi-variational inequalities is also shown. The corresponding experimental results support our theoretical findings.

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