A hybrid FR-DY conjugate gradient algorithm for unconstrained optimization with application in portfolio selection

Abubakar, Auwal Bala; Malik, Maulana; Chaipunya, Parin; Ibrahim, Abdulkarim Hassan

doi:10.3934/math.2021383

Cited by 25 publications

(16 citation statements)

References 26 publications

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“…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%

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: 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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“…Under the Lipschitz continuity of the gradient, the convergence prove of these methods was established with the weak Wolfe line search (4) and (5). For more reading on hybrid CG algorithms and application of the CG method can be referred to [18], [19].…”

Section: ∈ {0 }mentioning

confidence: 99%

A new hybrid conjugate gradient algorithm for optimization models and its application to regression analysis

Sulaiman

Bakar²,

Mamat³

et al. 2021

IJEECS

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The hybrid conjugate gradient (CG) method is among the efficient variants of CG method for solving optimization problems. This is due to their low memory requirements and nice convergence properties. In this paper, we present an efficient hybrid CG method for solving unconstrained optimization models and show that the method satisfies the sufficient descent condition. The global convergence prove of the proposed method would be established under inexact line search. Application of the proposed method to the famous statistical regression model describing the global outbreak of the novel COVID-19 is presented. The study parameterized the model using the weekly increase/decrease of recorded cases from December 30, 2019 to March 30, 2020. Preliminary numerical results on some unconstrained optimization problems show that the proposed method is efficient and promising. Furthermore, the proposed method produced a good regression equation for COVID-19 confirmed cases globally.

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“…Exploiting the simplicity and low storage requirement of the conjugate gradient method [1,2], in recent times, several authors have extended many conjugate gradient algorithms designed to solve unconstrained optimization problems to solve large-scale nonlinear equations (1.6) (see [3][4][5][6][7][8][9][10][11][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]36]). For instance, using the projection scheme of Solodov and Svaiter [35], Xiao and Zhu [38] extended the Hager and Zhang conjugate descent (CG DESCENT) method to solve (1.6).…”

Section: Introductionmentioning

confidence: 99%

"A descent three-term derivative-free method for signal reconstruction in compressive sensing"

Ibrahim¹,

ABUBAKAR²,

ABUBAKAR³

2022

CJM

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"Many real-world phenomena in engineering, economics, statistical inference, compressed sensing and machine learning involve finding sparse solutions to under-determined or ill-conditioned equations. Our interest in this paper is to introduce a derivative-free method for recovering sparse signal and blurred image arising in compressed sensing by solving a nonlinear equation involving a monotone operator. The global convergence of the proposed method is established under the assumptions of monotonicity and Lipschitz continuity of the underlying operator. Numerical experiments are performed to illustrate the efficiency of the proposed method in the reconstruction of sparse signals and blurred images."

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A hybrid FR-DY conjugate gradient algorithm for unconstrained optimization with application in portfolio selection

Cited by 25 publications

References 26 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 hybrid conjugate gradient algorithm for optimization models and its application to regression analysis

"A descent three-term derivative-free method for signal reconstruction in compressive sensing"

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