A Conjugate Gradient Algorithm under Yuan-Wei-Lu Line Search Technique for Large-Scale Minimization Optimization Models

Li, Xiangrong; Wang, Songhua; Jin, Zhongzhou; Pham, Hongtruong

doi:10.1155/2018/4729318

Cited by 10 publications

(4 citation statements)

References 12 publications

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“…Recently, Yuan et al [17] open up a new way by modifying the WWP line search technique and partly proved the global convergence of the PRP algorithm. Further results are obtained (see [18][19][20], etc.) by this technique.…”

Section: Introductionmentioning

confidence: 74%

A Descent Conjugate Gradient Algorithm for Optimization Problems and Its Applications in Image Restoration and Compression Sensing

Cao

Liu³

2020

Mathematical Problems in Engineering

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It is well known that the nonlinear conjugate gradient algorithm is one of the effective algorithms for optimization problems since it has low storage and simple structure properties. This motivates us to make a further study to design a modified conjugate gradient formula for the optimization model, and this proposed conjugate gradient algorithm possesses several properties: (1) the search direction possesses not only the gradient value but also the function value; (2) the presented direction has both the sufficient descent property and the trust region feature; (3) the proposed algorithm has the global convergence for nonconvex functions; (4) the experiment is done for the image restoration problems and compression sensing to prove the performance of the new algorithm.

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Section: Introductionmentioning

confidence: 74%

A Descent Conjugate Gradient Algorithm for Optimization Problems and Its Applications in Image Restoration and Compression Sensing

Cao

Liu³

2020

Mathematical Problems in Engineering

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“…The sufficient descent property with a constant ܿ 0 ݀ ௦ ் ݃ ௦ െܿ ∥ ݃ ௦ ∥ ଶ ሺ7ሻ (7) plays a crucial role in convergence for the CG methods including the PRP algorithm (see [4][10] [13][14]). To have this property, Grippo and Lucidi [19].…”

Section: Introductionmentioning

confidence: 99%

A Conjugate Gradient Algorithm Based on Cable-Stayed Bridges Model for Nonconvex Minimization

Lin,

Zhou,

Qin

et al. 2023

Advances in Transdisciplinary Engineering

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This paper examines the optimization problem of cable force in the construction phase of single-tower cable-stayed bridges, transforming it into an unconstrained problem that aims to control the vertical displacement of main beam nodes and the horizontal displacement of tower nodes. By introducing penalty terms, the constrained optimization problem is converted into an unconstrained one. The conjugate gradient algorithm is adopted to solve the unconstrained problem due to its simplicity, low storage requirement, and effectiveness in various engineering applications such as image restoration and financial modeling. However, under the Wolfe-Powell inexact line search, the global convergence of this algorithm usually depends on a Lipschitz continuity condition for convex/nonconvex functions. This paper investigates whether this condition can be relaxed, and analyzes the direction suggested by Yuan and Zhang (JCAM, 2005) for unconstrained problems. The paper features a designed conjugate gradient algorithm, iteration directions that guarantee sufficient descent and trust region properties, and proof of global convergence without the Lipschitz continuity condition. Numerical experiments are performed for optimization problems, image restoration, and the Muskingum model.

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“…to ensure the scalar ≥ 0. At present, there are many results obtained in CG algorithms (see [11,[18][19][20][21][22][23][24][25][26], etc.) and a modified weak Wolfe-Powell line search technique is presented to study open unconstrained optimization (see [27,28]).…”

Section: Introductionmentioning

confidence: 99%

A Three-Term Conjugate Gradient Algorithm with Quadratic Convergence for Unconstrained Optimization Problems

Yuan

2018

Mathematical Problems in Engineering

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This paper further studies the WYL conjugate gradient (CG) formula with ≥ 0 and presents a three-term WYL CG algorithm, which has the sufficiently descent property without any conditions. The global convergence and the linear convergence are proved; moreover the n-step quadratic convergence with a restart strategy is established if the initial step length is appropriately chosen. Numerical experiments for large-scale problems including the normal unconstrained optimization problems and the engineer problems (Benchmark Problems) show that the new algorithm is competitive with the other similar CG algorithms.

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A Conjugate Gradient Algorithm under Yuan-Wei-Lu Line Search Technique for Large-Scale Minimization Optimization Models

Cited by 10 publications

References 12 publications

A Descent Conjugate Gradient Algorithm for Optimization Problems and Its Applications in Image Restoration and Compression Sensing

A Descent Conjugate Gradient Algorithm for Optimization Problems and Its Applications in Image Restoration and Compression Sensing

A Conjugate Gradient Algorithm Based on Cable-Stayed Bridges Model for Nonconvex Minimization

A Three-Term Conjugate Gradient Algorithm with Quadratic Convergence for Unconstrained Optimization Problems

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