A modified conjugate gradient method for monotone nonlinear equations with convex constraints

Awwal, Aliyu Muhammed; Abubakar, Auwal Bala

doi:10.1016/j.apnum.2019.05.012

Cited by 48 publications

(35 citation statements)

References 28 publications

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“…In this section, in our numerical experiments, we consider 8 problems to implement our proposed method and make comparison with MHSP [25] method and PDY [45] method.…”

Section: Numerical Experiments and Applicationmentioning

confidence: 99%

“…In this subsection, to apply our proposed method in the numerical experiments, we consider the following 8 examples which are the samples in the related works of several references. Meanwhile, we make a numerical comparison of our method with MHSP [25] method and PDY [45] method. Both of the two methods have good performance in numerical experiments, and specially PDY method is well known for its stable performance on many problems.…”

Section: A Numerical Experimentsmentioning

confidence: 99%

“…The parameters of MHSP method and PDY method are chosen from [25] and [45] respectively. In MSGP method, we set the parameter σ = 0.001, λ = 1, ρ = 0.8, µ = 0.85 and ν = 0.001.…”

Section: A Numerical Experimentsmentioning

confidence: 99%

“…By modifying the search direction to be sufficiently descent, their method performs more effectively in numerical experiments. Subsequently, Awwal et al [25] proposed a modified Hestenes-Stiefel (HS) spectral conjugate gradient (CG) method to solve monotone non-linear equations with convex constraints efficiently. Xiao and Zhu [26] combined the CG-Descent method [27] and projection method to improve the algorithm in the numerical experiments and applied their work to solve L 1 -norm problem in image deconvolution problems.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, inspired by the works of [24] and [25], we further investigate the projection method with a modified SG parameter and propose a derivative free algorithm for solving non-linear monotone equations with convex constraints. The aim of this work is to improve the efficiency of the projection method and expand the scope of its applications.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Modified Spectral Gradient Projection Method for Solving Non-linear Monotone Equations with Convex Constraints and Its Application

2020

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In this paper, we propose a derivative free algorithm for solving non-linear monotone equations with convex constraints. The proposed algorithm combines the method of spectral gradient and the projection method. We also modify the backtracking line search technique. The global convergence of the proposed method is guaranteed, under the mild conditions. Further, the numerical experiments show that the largescale non-linear equations with convex constraints can be effectively solved with our method. The L 1-norm regularized problems in signal reconstruction are studied by using our method.

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“…In this section, in our numerical experiments, we consider 8 problems to implement our proposed method and make comparison with MHSP [25] method and PDY [45] method.…”

Section: Numerical Experiments and Applicationmentioning

confidence: 99%

Section: A Numerical Experimentsmentioning

confidence: 99%

“…The parameters of MHSP method and PDY method are chosen from [25] and [45] respectively. In MSGP method, we set the parameter σ = 0.001, λ = 1, ρ = 0.8, µ = 0.85 and ν = 0.001.…”

Section: A Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Modified Spectral Gradient Projection Method for Solving Non-linear Monotone Equations with Convex Constraints and Its Application

2020

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Parameter Conjugate Gradient with Secant Equation Based Elman Neural Network and its Convergence Analysis

Fan

Zhang

Huang

2022

Advcd Theory and Sims

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Elman neural network (ENN) is one of the local recursive networks with a feedback mechanism. The parameter conjugate gradient method is a promising alternative to the gradient descent method, due to its faster convergence speed that results from searching for the conjugate descent direction with an adaptive step size (obtained by Wolfe conditions). However, there are still some challenges such as how to avoid the sawtooth phenomenon in gradient algorithms to improve the learning accuracy of the second-order curvature of an objective function. As such, this paper presents a novel parametric conjugate gradient method that is based on the secant equation for training ENN in an effective way. Strict proof of the theoretical convergence of the proposed algorithm is provided in detail. In particular, the weak convergence and strong convergence of the algorithm, as well as the monotonicity of the error function are proved. Except for the theoretical analysis, the three numerical experiments have been conducted by applying the algorithm to three problems of classification, regression, and function approximation on nine real-world datasets. The experimental results have demonstrated the feasibility of the proposed algorithm and the correctness of this theoretical analysis.

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Two derivative‐free algorithms for constrained nonlinear monotone equations

Abubakar

Mohammad

Waziri

2021

Comp and Math Methods

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We propose two positive parameters based on the choice of Birgin and Martínez search direction. Using the two classical choices of the Barzilai-Borwein parameters, two positive parameters were derived by minimizing the distance between the relative matrix corresponding to the propose search direction and the scaled memory-less Broyden-Fletcher-Goldfarb-Shanno (BFGS) matrix in the Frobenius norm. Moreover, the resulting direction is descent independent of any line search condition. We established the global convergence of the proposed algorithm under some appropriate assumptions. In addition, numerical experiments on some benchmark test problems are reported in order to show the efficiency of the proposed algorithm.

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A modified conjugate gradient method for monotone nonlinear equations with convex constraints

Cited by 48 publications

References 28 publications

A Modified Spectral Gradient Projection Method for Solving Non-linear Monotone Equations with Convex Constraints and Its Application

A Modified Spectral Gradient Projection Method for Solving Non-linear Monotone Equations with Convex Constraints and Its Application

Parameter Conjugate Gradient with Secant Equation Based Elman Neural Network and its Convergence Analysis

Two derivative‐free algorithms for constrained nonlinear monotone equations

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