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An efficient DY-type spectral conjugate gradient method for system of nonlinear monotone equations with application in signal recovery
- Source :
- AIMS Mathematics, Vol 6, Iss 8, Pp 8078-8106 (2021)
- Publication Year :
- 2021
- Publisher :
- AIMS Press, 2021.
-
Abstract
- Many problems in engineering and social sciences can be transformed into system of nonlinear equations. As a result, a lot of methods have been proposed for solving the system. Some of the classical methods include Newton and Quasi Newton methods which have rapid convergence from good initial points but unable to deal with large scale problems due to the computation of Jacobian matrix or its approximation. Spectral and conjugate gradient methods proposed for unconstrained optimization, and later on extended to solve nonlinear equations do not require any computation of Jacobian matrix or its approximation, thus, are suitable to handle large scale problems. In this paper, we proposed a spectral conjugate gradient algorithm for solving system of nonlinear equations where the operator under consideration is monotone. The search direction of the proposed algorithm is constructed by taking the convex combination of the Dai-Yuan (DY) parameter and a modified conjugate descent (CD) parameter. The proposed search direction is sufficiently descent and under some suitable assumptions, the global convergence of the proposed algorithm is proved. Numerical experiments on some test problems are presented to show the efficiency of the proposed algorithm in comparison with an existing one. Finally, the algorithm is successfully applied in signal recovery problem arising from compressive sensing.
- Subjects :
- Computer science
General Mathematics
Computation
MathematicsofComputing_NUMERICALANALYSIS
Nonlinear system
symbols.namesake
Compressed sensing
Monotone polygon
Conjugate gradient method
conjugate gradient method
Convergence (routing)
Jacobian matrix and determinant
symbols
QA1-939
Applied mathematics
Convex combination
nonlinear monotone equations
Mathematics
spectral conjugate gradient method and large-scale problems
Subjects
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 6
- Issue :
- 8
- Database :
- OpenAIRE
- Journal :
- AIMS Mathematics
- Accession number :
- edsair.doi.dedup.....e12f784ce2c60fd8bbe4cfa489ce8fb6