Improved Dai-Yuan iterative schemes for convex constrained monotone nonlinear systems

Two new Dai-Yuan (DY) iterative schemes are presented in this article for solving constrained system of nonlinear monotone equations. Using an extension of the classical scheme by Dai and Yuan [Soc. Ind. Appl. Math., 10(1)(1999) 177-182], two modified DY search directions are obtained, which possess...

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Published in:Mathematical sciences (Karaj, Iran) Vol. 18; no. 4; pp. 707 - 728
Main Authors: Ahmed, Kabiru, Waziri, Mohammed Yusuf, Halilu, Abubakar Sani, Sabi’u, Jamilu, Murtala, Salisu, Abdullahi, Habibu
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2024
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Constraints
Convergence
Eigenvalues
Mathematics
Mathematics and Statistics
Methods
Nonlinear systems
Optimization
Original Research
Parameter modification
Conjugacy condition
Projection operator
Convex set
90C30
Non-smooth functions
Backtracking technique
Descent condition
90C26
94A12
ISSN:2008-1359, 2251-7456
Online Access:Get full text
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Abstract Two new Dai-Yuan (DY) iterative schemes are presented in this article for solving constrained system of nonlinear monotone equations. Using an extension of the classical scheme by Dai and Yuan [Soc. Ind. Appl. Math., 10(1)(1999) 177-182], two modified DY search directions are obtained, which possess the vital property for analyzing global convergence. By conducting eigenvalue analysis, appropriate values were obtained for the nonnegative parameter C of the two schemes. The self-restarting structure of the first scheme, as well as the choices of the parameter C in both methods, ensure fast convergence to the solution of the problems considered. Algorithms of both schemes are implemented by employing monotone line search procedure by Zhang and Zhou [J. Comput. Appl. Math. 196(2006) 478-484] and the projection technique. Using fundamental assumptions, global convergence of both schemes is established and results of numerical experiments with four recent methods in the literature show that the new methods are encouraging.
AbstractList Two new Dai-Yuan (DY) iterative schemes are presented in this article for solving constrained system of nonlinear monotone equations. Using an extension of the classical scheme by Dai and Yuan [Soc. Ind. Appl. Math., 10(1)(1999) 177-182], two modified DY search directions are obtained, which possess the vital property for analyzing global convergence. By conducting eigenvalue analysis, appropriate values were obtained for the nonnegative parameter C of the two schemes. The self-restarting structure of the first scheme, as well as the choices of the parameter C in both methods, ensure fast convergence to the solution of the problems considered. Algorithms of both schemes are implemented by employing monotone line search procedure by Zhang and Zhou [J. Comput. Appl. Math. 196(2006) 478-484] and the projection technique. Using fundamental assumptions, global convergence of both schemes is established and results of numerical experiments with four recent methods in the literature show that the new methods are encouraging.
Two new Dai-Yuan (DY) iterative schemes are presented in this article for solving constrained system of nonlinear monotone equations. Using an extension of the classical scheme by Dai and Yuan [Soc. Ind. Appl. Math., 10(1)(1999) 177-182], two modified DY search directions are obtained, which possess the vital property for analyzing global convergence. By conducting eigenvalue analysis, appropriate values were obtained for the nonnegative parameter C of the two schemes. The self-restarting structure of the first scheme, as well as the choices of the parameter C in both methods, ensure fast convergence to the solution of the problems considered. Algorithms of both schemes are implemented by employing monotone line search procedure by Zhang and Zhou [J. Comput. Appl. Math. 196(2006) 478-484] and the projection technique. Using fundamental assumptions, global convergence of both schemes is established and results of numerical experiments with four recent methods in the literature show that the new methods are encouraging.
Author Halilu, Abubakar Sani
Abdullahi, Habibu
Murtala, Salisu
Ahmed, Kabiru
Waziri, Mohammed Yusuf
Sabi’u, Jamilu
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  givenname: Mohammed Yusuf
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  givenname: Abubakar Sani
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  surname: Abdullahi
  fullname: Abdullahi, Habibu
  email: habibu.abdullahi@slu.edu.ng
  organization: Department of Mathematics, Sule Lamido University, Numerical Optimization Research Group, Bayero University
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Keywords Conjugacy condition
Projection operator
Convex set
90C30
Non-smooth functions
Backtracking technique
Descent condition
90C26
94A12
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Snippet Two new Dai-Yuan (DY) iterative schemes are presented in this article for solving constrained system of nonlinear monotone equations. Using an extension of the...
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SubjectTerms Algorithms
Applications of Mathematics
Constraints
Convergence
Eigenvalues
Mathematics
Mathematics and Statistics
Methods
Nonlinear systems
Optimization
Original Research
Parameter modification
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Title Improved Dai-Yuan iterative schemes for convex constrained monotone nonlinear systems
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