Global convergence of BFGS and PRP methods under a modified weak Wolfe–Powell line search

Yuan, Gonglin; Wei, Zengxin; Lu, Xiwen

doi:10.1016/j.apm.2017.02.008

Cited by 93 publications

(65 citation statements)

References 53 publications

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“…Figures 1 and 2 show that the performance of Algorithm 1 is the best and that Algorithm 1 has the best robust property among those three methods and Algorithm 2 is better than Algorithm 3, which shows that the given formula (7) is competitive to the normal three-term conjugate gradient formula (20) and the YWL line search technique is more effective than the norm WWP technique, and all of these conclusions are coincident with the results of [9]. Algorithm 1 in Figure 3 is competitive to the other two algorithms and it has the best robust property.…”

Section: Results and Discussion We Use The Tool Of Dolan Andsupporting

confidence: 68%

“…By Lemma 2 and Assumption A, similar to [9], it is not difficult to show that the YWL line search technique is reasonable and Algorithm 1 is well defined. Here, we do not state it anymore.…”

Section: Lemmamentioning

confidence: 99%

“…Inequality (8) shows that the new formula has a sufficient descent property and inequality (9) proves that the new formula possesses a trust region feature. Both of these properties (8) and (9) are good theory characters and they play an important role in the global convergence of a conjugate gradient algorithm.…”

Section: Lemmamentioning

confidence: 99%

“…At present, there exist many good conjugate gradients (see [6][7][8], etc.). Yuan, Wei, and Lu [9] gave a modified weak Wolfe-Powell (we called it YWL) line search for steplength designed by…”

Section: Introductionmentioning

confidence: 99%

“…It is well known that there exist two open problems which are the global convergence of the normal BFGS method and the global convergence of the PRP method for nonconvex functions under the inexact line search technique, where the first problem is regarded as one of the most difficult one thousand mathematical problems of the 20th century [10]. Yuan et al [9] partly solved these two open problems under the YWL technique, and the numerical performance shows that the YWL technique is more competitive than the normal weak Wolfe-Powell technique. Further study work can be found in their paper [11].…”

Section: Introductionmentioning

confidence: 99%

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

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Mathematical Problems in Engineering

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This paper gives a modified Hestenes and Stiefel (HS) conjugate gradient algorithm under the Yuan-Wei-Lu inexact line search technique for large-scale unconstrained optimization problems, where the proposed algorithm has the following properties: (1) the new search direction possesses not only a sufficient descent property but also a trust region feature; (2) the presented algorithm has global convergence for nonconvex functions; (3) the numerical experiment showed that the new algorithm is more effective than similar algorithms.

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Section: Results and Discussion We Use The Tool Of Dolan Andsupporting

confidence: 68%

Section: Lemmamentioning

confidence: 99%

Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

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An improved descent Perry‐type algorithm for large‐scale unconstrained nonconvex problems and applications to image restoration problems

Wang,

Lv,

2024

Numerical Linear Algebra App

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Conjugate gradient methods are much effective for large‐scale unconstrained optimization problems by their simple computations and low memory requirements. The Perry conjugate gradient method has been considered to be one of the most efficient methods in the context of unconstrained minimization. However, a globally convergent result for general functions has not been established yet. In this paper, an improved three‐term Perry‐type algorithm is proposed which automatically satisfies the sufficient descent property independent of the accuracy of line search strategy. Under the standard Wolfe line search technique and a modified secant condition, the proposed algorithm is globally convergent for general nonlinear functions without convexity assumption. Numerical results compared with the Perry method for stability, two modified Perry‐type conjugate gradient methods and two effective three‐term conjugate gradient methods for large‐scale problems up to 300,000 dimensions indicate that the proposed algorithm is more efficient and reliable than the other methods for the testing problems. Additionally, we also apply it to some image restoration problems.

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A Modified Dai-Yuan Conjugate Gradient Algorithm for Large-Scale Optimization Problems

Yuan

2018

Cloud Computing and Security

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Global convergence of BFGS and PRP methods under a modified weak Wolfe–Powell line search

Cited by 93 publications

References 53 publications

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

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

An improved descent Perry‐type algorithm for large‐scale unconstrained nonconvex problems and applications to image restoration problems

A Modified Dai-Yuan Conjugate Gradient Algorithm for Large-Scale Optimization Problems

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