A Modified Three-Term Conjugate Descent Derivative-Free Method for Constrained Nonlinear Monotone Equations and Signal Reconstruction Problems

Aliyu Yusuf, Nibron Haggai Manjak and Maggie Aphane ()
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Aliyu Yusuf: Department of Science, School of Continuing Education, Bayero University, BUK, Kano PMB 3011, Nigeria
Nibron Haggai Manjak: Department of Mathematical Sciences, Faculty of Science, Abubakar Tafawa Balewa University, Bauchi PMB 0248, Nigeria
Maggie Aphane: Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria 0204, South Africa

Mathematics, 2024, vol. 12, issue 11, 1-21

Abstract: Iterative methods for solving constraint nonlinear monotone equations have been developed and improved by many researchers. The aim of this research is to present a modified three-term conjugate descent (TTCD) derivative-free method for constrained nonlinear monotone equations. The proposed algorithm requires low storage memory; therefore, it has the capability to solve large-scale nonlinear equations. The algorithm generates a descent and bounded search direction d k at every iteration independent of the line search. The method is shown to be globally convergent under monotonicity and Lipschitz continuity conditions. Numerical results show that the suggested method can serve as an alternative to find the approximate solutions of nonlinear monotone equations. Furthermore, the method is promising for the reconstruction of sparse signal problems.

Keywords: constrained nonlinear monotone equations; derivative-free method; global convergence; numerical experiments; signal reconstruction problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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