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150 results on '"Abubakar, Auwal Bala"'

8. A Dai-Liao-type projection method for monotone nonlinear equations and signal processing

Author

Ibrahim Abdulkarim Hassan, Kumam Poom, Abubakar Auwal Bala, Abdullahi Muhammad Sirajo, and Mohammad Hassan

Subjects
nonlinear equations, unconstrained optimization, conjugate gradient method, projection method, compressive sensing, 90c30, 65k05, 90c53, 49m37, 15a18, Mathematics, QA1-939
Abstract

In this article, inspired by the projection technique of Solodov and Svaiter, we exploit the simple structure, low memory requirement, and good convergence properties of the mixed conjugate gradient method of Stanimirović et al. [New hybrid conjugate gradient and broyden-fletcher-goldfarbshanno conjugate gradient methods, J. Optim. Theory Appl. 178 (2018), no. 3, 860–884] for unconstrained optimization problems to solve convex constrained monotone nonlinear equations. The proposed method does not require Jacobian information. Under monotonicity and Lipschitz continuity assumptions, the global convergence properties of the proposed method are established. Computational experiments indicate that the proposed method is computationally efficient. Furthermore, the proposed method is applied to solve the ℓ1{\ell }_{1}-norm regularized problems to decode sparse signals and images in compressive sensing.

Published
2022
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30. Extended modified three-term conjugate gradient method for large-scale nonlinear equations.

Author

Deepho, Jitsupa, Malik, Maulana, and Abubakar, Auwal Bala

Subjects
CONJUGATE gradient methods, NONLINEAR equations, NONSMOOTH optimization
Abstract

In this research paper, we introduce a novel gradient-free modified three-term conjugate gradient method designed to solve nonlinear equations subject to convex constraints. Our approach incorporates the projection scheme, which enhances the effectiveness of the proposed method. Building upon the modified three-term conjugate gradient method for solving M-tensor systems and ℓ1-norm-based nonsmooth optimization problems, our method can be regarded as an extension of their technique. By making mild assumptions, we establish the theoretical convergence properties of our iterative method. Through extensive numerical experiments, we demonstrate that our proposed approach is not only highly efficient but also outperforms other existing methods in terms of performance and accuracy. [ABSTRACT FROM AUTHOR]

Published
2023
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43. A new family of hybrid three-term conjugate gradient method for unconstrained optimization with application to image restoration and portfolio selection.

Author

Malik, Maulana, Sulaiman, Ibrahim Mohammed, Abubakar, Auwal Bala, Ardaneswari, Gianinna, and Sukono

Subjects
CONJUGATE gradient methods, MATHEMATICAL optimization, IMAGE reconstruction, STOCHASTIC convergence, PORTFOLIO management (Investments)
Abstract

The conjugate gradient (CG) method is an optimization method, which, in its application, has a fast convergence. Until now, many CG methods have been developed to improve computational performance and have been applied to real-world problems. In this paper, a new hybrid three-term CG method is proposed for solving unconstrained optimization problems. The search direction is a threeterm hybrid form of the Hestenes-Stiefel (HS) and the Polak-Ribi'ere-Polyak (PRP) CG coefficients, and it satisfies the sufficient descent condition. In addition, the global convergence properties of the proposed method will also be proved under the weak Wolfe line search. By using several test functions, numerical results show that the proposed method is most efficient compared to some of the existing methods. In addition, the proposed method is used in practical application problems for image restoration and portfolio selection. [ABSTRACT FROM AUTHOR]

Published
2023
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