Derivative-free HS-DY-type method for solving nonlinear equations and image restoration

Abubakar, Auwal Bala; Ibrahim, Abdulkarim Hassan; Rilwan, Jewaidu

doi:10.1016/j.heliyon.2020.e05400

Cited by 23 publications

(15 citation statements)

References 31 publications

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“…Assume that T (v k ) ̸ = 0 for all k, and consequently p k ̸ = 0 from Lemma 2.4. In the following, we show that the line search procedure (7) always terminates in a finite number of steps. If θ k ̸ = ζ, then ζ −1 θ k does not satisfy (7).…”

Section: By Adding the Above Equations Formentioning

confidence: 94%

“…Considering the simplicity and low storage requirement of the conjugate gradient method [20,21], several researchers combined the projection technique of Solodov and Svaiter [56] with the conjugate gradient methods to solve large-scale nonlinear equations, see [38,13,42,40,43,1,7,45,41,12,47,10,9,46,39,52,2,3,8,53,11,37,44,4,6,36] and references therein. Based on the projection method, Gao and He [35] introduced an efficient three-term derivative-free method for solving nonlinear monotone equations with convex constraints (1) by choosing a part of the Liu-Storey (LS) conjugate parameter as a new conjugate parameter.…”

Section: Introductionmentioning

confidence: 99%

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Projection method with inertial step for nonlinear equations: Application to signal recovery

Ibrahim

Sun

Chaipunya

et al. 2023

JIMO

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<p style='text-indent:20px;'>In this paper, using the concept of inertial extrapolation, we introduce a globally convergent inertial extrapolation method for solving nonlinear equations with convex constraints for which the underlying mapping is monotone and Lipschitz continuous. The method can be viewed as a combination of the efficient three-term derivative-free method of Gao and He [Calcolo. 55(4), 1-17, 2018] with the inertial extrapolation step. Moreover, the algorithm is designed such that at every iteration, the method is free from derivative evaluations. Under standard assumptions, we establish the global convergence results for the proposed method. Numerical implementations illustrate the performance and advantage of this new method. Moreover, we also extend this method to solve the LASSO problems to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of our algorithm.</p>

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Section: By Adding the Above Equations Formentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Projection method with inertial step for nonlinear equations: Application to signal recovery

Ibrahim

Sun

Chaipunya

et al. 2023

JIMO

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“…To achieve the boundedness of their proposed direction, they modified one of the directions defined in [25]. For more recent articles on derivative-free iterative methods for solving (1), readers can refer to [26]- [42] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A New Three-Term Hestenes-Stiefel Type Method for Nonlinear Monotone Operator Equations and Image Restoration

et al. 2021

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In this article, a derivative-free method of Hestenes-Stiefel type is proposed for solving system of monotone operator equations with convex constraints. The method proposed is matrix-free, and its sequence of search directions are bounded and satisfies the sufficient descent condition. The global convergence of the proposed approach is established under the assumptions that the underlying operator is monotone and Lipschitz continuous. Numerical experiment results are reported to show the efficiency of the proposed method. Furthermore, to illustrate the applicability of the proposed method, it is used in restoring blurred images.INDEX TERMS Derivative-free algorithm, Monotone operator equations, projection technique, image restoration.

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“…However, to establish the convergence of the method, Li and Zheng assume that the operator is uniformly monotone which is a stronger condition. Some other related ideas on spectral gradient-type and spectral conjugate gradient-type methods for finding solution to (1) were studied in [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A Modified Scaled Spectral-Conjugate Gradient-Based Algorithm for Solving Monotone Operator Equations

Abubakar

Muangchoo

Ibrahim

et al. 2021

Journal of Mathematics

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This paper proposes a modified scaled spectral-conjugate-based algorithm for finding solutions to monotone operator equations. The algorithm is a modification of the work of Li and Zheng in the sense that the uniformly monotone assumption on the operator is relaxed to just monotone. Furthermore, unlike the work of Li and Zheng, the search directions of the proposed algorithm are shown to be descent and bounded independent of the monotonicity assumption. Moreover, the global convergence is established under some appropriate assumptions. Finally, numerical examples on some test problems are provided to show the efficiency of the proposed algorithm compared to that of Li and Zheng.

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Derivative-free HS-DY-type method for solving nonlinear equations and image restoration

Cited by 23 publications

References 31 publications

Projection method with inertial step for nonlinear equations: Application to signal recovery

Projection method with inertial step for nonlinear equations: Application to signal recovery

A New Three-Term Hestenes-Stiefel Type Method for Nonlinear Monotone Operator Equations and Image Restoration

A Modified Scaled Spectral-Conjugate Gradient-Based Algorithm for Solving Monotone Operator Equations

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