New hybrid three-term spectral-conjugate gradient method for finding solutions of nonlinear monotone operator equations with applications

Abubakar, Auwal Bala; Ibrahim, Abdulkarim Hassan; Chaipunya, Parin; Rano, Sadiya Ali

doi:10.1016/j.matcom.2021.07.005

Cited by 18 publications

(14 citation statements)

References 31 publications

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“…Nonlinear monotone equations also arise in signal and image recovery problems. Due to their simplicity and low storage requirements [38], CG-type algorithms are currently widely used to solve (1). It also generates sequence of iterates {x k } via…”

Section: Introductionmentioning

confidence: 99%

A Modified Hybrid DYHS Type Conjugate Gradient Algorithm for Solving Nonlinear Monotone Equations and Signal Recovery Problems

Yusuf

Manjak

Kwami

et al. 2023

Preprint

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In this research, a modified hybrid Dai-Yuan and Hestenes-Stiefel (DYHS) conjugate gradient (CG) algorithm is presented, with develops sufficient descent property. The hyperplane projection method is also used and the algorithm is a convex combination of DY and HS parameters. With some reasonable assumptions, the global convergence property is obtained under accelerated step size. The numerical experiment demonstrate that the DYHS algorithm is more effective and robust than other existing methods for solving nonlinear monotone equations and signal recovery problems. Mathematics Subject Classification: 65K05, 90C52, 90C26

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Section: Introductionmentioning

confidence: 99%

A Modified Hybrid DYHS Type Conjugate Gradient Algorithm for Solving Nonlinear Monotone Equations and Signal Recovery Problems

Yusuf

Manjak

Kwami

et al. 2023

Preprint

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“…The CG-type methods are popular nowadays for solving (1), because of their simplicity and low storage requirements. Precisely, the hybridization of CG methods is currently an interesting approach used to design an efficient algorithms for solving (1).…”

Section: Introductionmentioning

confidence: 99%

“…In [16], the authors presented a hybrid CG algorithm in which the hybridized parameter contains the modified versions of the Hestenes-Stiefel and Polak-Ribiére-Polyak CG parameters. Waziri et al [24] considered an improved CG-like algorithm for solving (1) via the convex hybridization of the Fletcher-Reeves (FR) and Polak-Ribiére-Polyak (PRP) parameters. The hybrid method was proven to converge globally and numerically efficient.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, by the well-known effectiveness of FR-CG method, Danmalam et al [9] proposed, analyzed and implemented a hybrid conjugate residual projection algorithm based on the convex hybridization of two CG parameters. Quite a number of hybrid algorithms for solving (1) have been presented by many researchers, see the following papers [1,3,15,27] for recent results. Specifically, the PRP method, the DY-type method, the HS-type method, and the FR method were described as special cases for the hybrid CG approach proposed in [1].…”

Section: Introductionmentioning

confidence: 99%

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A solution method for nonlinear monotone equations via hybrid spectral conjugate gradient and signal recovery problems

Yusuf

Manjak

Mohammad

et al. 2023

Preprint

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In this paper, we propose a solution method via hybrid spectral conjugate gradient and signal recovery problem (ANHSCG) to solve nonlinear monotone equations. This has been done using the hybrid conjugate gradient (CG) parameters of Dai-Yuan (DY), conjugate descent (CD), Hestenes-Stiefel (HS), Liu-Storey (LS) and the corresponding search direction of spectral conjugate gradient method. The search direction has proved to be adequately descent regardless of the step-size. Under reasonable assumptions, the convergence of the algorithm is established. Additionally, numerical tests are run on a set of benchmark test problems to illustrate the effectiveness and competitiveness of the new algorithm compared with other existing alternatives. Finally, some applications of the proposed algorithm is explored. Mathematics Subject Classification: 65K05, 90C52, 90C26

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“…More precisely, the CG method has been paid attention to as an effective numerical method for solving large‐scale unconstrained optimization problems because of its simplicity and low storage 7,8 . Thus, using the projection technique in Solodov and Svaiter, 9 several researchers extended these methods resulting in derivative‐free methods (see References 10‐33 and references therein). Recently, based on Hestenes–Stiefel (HS) CG method 34 for unconstrained optimization, Wang et al 35 proposed a self‐adaptive three‐term derivative‐free method for solving monotone nonlinear equations with convex constraints.…”

Section: Introductionmentioning

confidence: 99%

Accelerated derivative‐free method for nonlinear monotone equations with an application

Ibrahim

Abubakar

Adamu

2021

Numerical Linear Algebra App

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In optimization theory, to speed up the convergence of iterative procedures, many mathematicians often use the inertial extrapolation method. In this article, based on the three‐term derivative‐free method for solving monotone nonlinear equations with convex constraints [Calcolo, 2016;53(2):133‐145], we design an inertial algorithm for finding the solutions of nonlinear equation with monotone and Lipschitz continuous operator. The convergence analysis is established under some mild conditions. Furthermore, numerical experiments are implemented to illustrate the behavior of the new algorithm. The numerical results have shown the effectiveness and fast convergence of the proposed inertial algorithm over the existing algorithm. Moreover, as an application, we extend this method to solve the LASSO problem to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of the method.

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New hybrid three-term spectral-conjugate gradient method for finding solutions of nonlinear monotone operator equations with applications

Cited by 18 publications

References 31 publications

A Modified Hybrid DYHS Type Conjugate Gradient Algorithm for Solving Nonlinear Monotone Equations and Signal Recovery Problems

A Modified Hybrid DYHS Type Conjugate Gradient Algorithm for Solving Nonlinear Monotone Equations and Signal Recovery Problems

A solution method for nonlinear monotone equations via hybrid spectral conjugate gradient and signal recovery problems

Accelerated derivative‐free method for nonlinear monotone equations with an application

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