A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing

Ibrahim Mohammed Sulaiman, Aliyu Muhammed Awwal, Maulana Malik, Nuttapol Pakkaranang () and Bancha Panyanak ()
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Ibrahim Mohammed Sulaiman: Institute of Strategic Industrial Decision Modelling (ISIDM), School of Quantitative Sciences, Universiti Utara Malaysia (UUM), Sintok 06010, Malaysia
Aliyu Muhammed Awwal: Department of Mathematics, Faculty of Science, Gombe State University (GSU), Gombe 760214, Nigeria
Maulana Malik: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia (UI), Depok 16424, Indonesia
Nuttapol Pakkaranang: Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand
Bancha Panyanak: Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2022, vol. 10, issue 16, 1-17

Abstract: Nonlinear systems of equations are widely used in science and engineering and, therefore, exploring efficient ways to solve them is paramount. In this paper, a new derivative-free approach for solving a nonlinear system of equations with convex constraints is proposed. The search direction of the proposed method is derived based on a modified conjugate gradient method, in such a way that it is sufficiently descent. It is worth noting that, unlike many existing methods that require a monotonicity assumption to prove the convergence result, our new method needs the underlying function to be pseudomonotone, which is a weaker assumption. The performance of the proposed algorithm is demonstrated on a set of some test problems and applications arising from compressive sensing. The obtained results confirm that the proposed method is effective compared to some existing algorithms in the literature.

Keywords: numerical algorithms; nonlinear problems; pseudomonotone function; projection method; global convergence; compressive sensing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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