PRP-like algorithm for monotone operator equations

2021 ◽  
Author(s):  
Auwal Bala Abubakar ◽  
Poom Kumam ◽  
Hassan Mohammad ◽  
Abdulkarim Hassan Ibrahim
Keyword(s):  
Monotone Operator ◽  
Operator Equations

A derivative-free iterative method for nonlinear ill-posed equations with monotone operators

2017 ◽  
Vol 25 (5) ◽  
pp. 543-551 ◽  
Author(s):  
Santhosh George ◽  
M. Thamban Nair
Keyword(s):  
Iterative Method ◽  
Convergence Analysis ◽  
Monotone Operator ◽  
Regularization Parameter ◽  
A Priori ◽  
Monotone Operators ◽  
Adaptive Procedure ◽  
Operator Equations ◽  
Derivative Free ◽  
Ill Posed

AbstractRecently, Semenova [12] considered a derivative free iterative method for nonlinear ill-posed operator equations with a monotone operator. In this paper, a modified form of Semenova’s method is considered providing simple convergence analysis under more realistic nonlinearity assumptions. The paper also provides a stopping rule for the iteration based on an a priori choice of the regularization parameter and also under the adaptive procedure considered by Pereverzev and Schock [11].

scholarly journals A Modified Scaled Spectral-Conjugate Gradient-Based Algorithm for Solving Monotone Operator Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Auwal Bala Abubakar ◽  
Kanikar Muangchoo ◽  
Abdulkarim Hassan Ibrahim ◽  
Sunday Emmanuel Fadugba ◽  
Kazeem Olalekan Aremu ◽  
...  
Keyword(s):  
Global Convergence ◽  
Monotone Operator ◽  
Conjugate Gradient ◽  
Test Problems ◽  
Operator Equations ◽  
Numerical Examples ◽  
Monotonicity Assumption ◽  
Gradient Based ◽  
Spectral Conjugate Gradient ◽  
Search Directions

This paper proposes a modified scaled spectral-conjugate-based algorithm for finding solutions to monotone operator equations. The algorithm is a modification of the work of Li and Zheng in the sense that the uniformly monotone assumption on the operator is relaxed to just monotone. Furthermore, unlike the work of Li and Zheng, the search directions of the proposed algorithm are shown to be descent and bounded independent of the monotonicity assumption. Moreover, the global convergence is established under some appropriate assumptions. Finally, numerical examples on some test problems are provided to show the efficiency of the proposed algorithm compared to that of Li and Zheng.

scholarly journals A New Three-Term Hestenes-Stiefel Type Method for Nonlinear Monotone Operator Equations and Image Restoration

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 18262-18277
Author(s):  
Auwal Bala Abubakar ◽  
Kanikar Muangchoo ◽  
Abdulkarim Hassan Ibrahim ◽  
Abubakar Bakoji Muhammad ◽  
Lateef Olakunle Jolaoso ◽  
...  
Keyword(s):  
Image Restoration ◽  
Monotone Operator ◽  
Operator Equations ◽  
Type Method
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