A hybrid HS-LS conjugate gradient algorithm for unconstrained optimization with applications in motion control and image recovery

Abubakar, Auwal Bala; Malik, Maulana; Ibrahim, Abdulkarim Hassan; Pakkaranang, Nuttapol; Panyanak, Bancha

doi:10.1016/j.cam.2023.115304

Cited by 5 publications

(10 citation statements)

References 36 publications

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“…In this section, we commence by outlining our formulation, followed by the presentation of our proposed algorithm. In a prior study by Kumam [25], they introduced a CG hybrid three-term method denoted as HTTHSLS, which incorporates the following search direction,…”

Section: Algorithm and Theoretical Resultsmentioning

confidence: 99%

“…By revisiting the proposed three-term LS and CD CG method by Kumam [25] and Deepho [15] respectively, which can be defined as,…”

Section: Algorithm and Theoretical Resultsmentioning

confidence: 99%

“…In this section, we conduct an analysis of the performance of our novel TTLC CG algorithm on 150 test functions sourced from Andrei [8], Moré [32], and Jamil [24]. The newly proposed method, denoted as TTLC, will be compared against several other methods, including NHS+ [26], HTTHSLS [25], TTCDDY [15], HTT [1], TTPRLS [2], HTHP [31] and TTRMIL [28]. All the comparative methods were implemented and executed using Matlab R2021B with Intel ® Core™ i5-9300H processor, 16 GB RAM, and 64-bit Windows 11 on a personal laptop.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…It has been proven to achieve global convergence under specific conditions and has demonstrated efficiency when compared to some previously proposed methods. In addition, Kumam [25] and Deepho [15] also have introduced modifications to the CG hybrid three-term approaches, involving combinations of HS and LS as well as CD and DY provided a scaled preconditioner to the hybrid parameters. These modifications leverage existing conjugate gradient parameters, yielding positive results in solving a variety of test problems for both approaches.…”

Section: Introductionmentioning

confidence: 99%

“…Inspires from the concepts elucidated in [1,15,25], we introduced a new CG hybrid threeterm approach designed for addressing the problem denoted as (1). Referred to as the Three-Term LS-CD (TTLC) method, new approach amalgamates the three-term LS and CD directions.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A New Hybrid Three-Term LS-CD Conjugate Gradient In Solving Unconstrained Optimization Problems

Ishak,

Marjugi

2024

MJMS

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The Conjugate Gradient (CG) method is renowned for its rapid convergence in optimization applications. Over the years, several modifications to CG methods have emerged to improve computational efficiency and tackle practical challenges. This paper presents a new three-term hybrid CG method for solving unconstrained optimization problems. This algorithm utilizes a search direction that combines Liu-Storey (LS) and Conjugate Descent (CD) CG coefficients and standardizes it using a spectral which acts as a scheme for the choices of the conjugate parameters. This resultant direction closely approximates the memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton direction, known for its bounded nature and compliance with the sufficient descent condition. The paper establishes the global convergence under standard Wolfe conditions and some appropriate assumptions. Additionally, the numerical experiments were conducted to emphasize the robustness and superior efficiency of this hybrid algorithm in comparison to existing approaches.

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Section: Algorithm and Theoretical Resultsmentioning

confidence: 99%

“…By revisiting the proposed three-term LS and CD CG method by Kumam [25] and Deepho [15] respectively, which can be defined as,…”

Section: Algorithm and Theoretical Resultsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Hybrid Three-Term LS-CD Conjugate Gradient In Solving Unconstrained Optimization Problems

Ishak,

Marjugi

2024

MJMS

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Global convergence via modified self-adaptive approach for solving constrained monotone nonlinear equations with application to signal recovery problems

Abdullahi¹

2023

RAIRO-Oper. Res.

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The conjugate gradient method (CG) is one of the most rapidly expanding and efficient ways for solving the unconstrained minimization problems. Recently, there has been a lot of effort into extending the CG approach to solve monotone nonlinear equations. For constrained monotone nonlinear equations, we describe a variation of the proposed method in this paper. The approach has a sufficient descent property, and its global convergence has been demonstrated with the help of some reasonable assumptions. Two sets of numerical tests were run to demonstrate the proposed method’s superior performance when compared to other methods. The initial experiment aimed to solve nonlinear equations with constraints, while in the second experiment, the method was applied to signal processing as well as issues with image recovery.

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An Improved Three-Term Conjugate Gradient Algorithm for Constrained Nonlinear Equations under Non-Lipschitz Conditions and Its Applications

Li,

Wang

2024

Mathematics

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This paper proposes an improved three-term conjugate gradient algorithm designed to solve nonlinear equations with convex constraints. The key features of the proposed algorithm are as follows: (i) It only requires that nonlinear equations have continuous and monotone properties; (ii) The designed search direction inherently ensures sufficient descent and trust-region properties, eliminating the need for line search formulas; (iii) Global convergence is established without the necessity of the Lipschitz continuity condition. Benchmark problem numerical results illustrate the proposed algorithm’s effectiveness and competitiveness relative to other three-term algorithms. Additionally, the algorithm is extended to effectively address the image denoising problem.

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A hybrid HS-LS conjugate gradient algorithm for unconstrained optimization with applications in motion control and image recovery

Cited by 5 publications

References 36 publications

A New Hybrid Three-Term LS-CD Conjugate Gradient In Solving Unconstrained Optimization Problems

A New Hybrid Three-Term LS-CD Conjugate Gradient In Solving Unconstrained Optimization Problems

Global convergence via modified self-adaptive approach for solving constrained monotone nonlinear equations with application to signal recovery problems

An Improved Three-Term Conjugate Gradient Algorithm for Constrained Nonlinear Equations under Non-Lipschitz Conditions and Its Applications

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