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Hybrid Nonlinear Conjugate Gradient Method For Unconstrained Optimization

Posted on:2024-01-16Degree:MasterType:Thesis
Country:ChinaCandidate:H GuoFull Text:PDF
GTID:2530307118486254Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
As one of the important methods of optimization theory,the conjugate gradient method is widely used in neural networks,image processing,finite element method and so on.The conjugate gradient method has a simple iteration format,good stability,and low storage requirements.These advantages can meet the requirements of big data processing and cloud computing in the information age.As a well-known conjugate gradient method with good theoretical properties and numerical performance,the Dai-Liao(DL)type conjugate gradient method has attracted many scholars to further study it in recent years.Based on the research of the DL-type conjugate gradient method,a DL-type hybrid conjugate gradient method and two hybrid spectral conjugate gradient methods are proposed in this thesis.(1)Based on the research of the DL-type conjugate gradient method,a hybrid conjugate parameter is constructed and a DL-type hybrid conjugate gradient methods is proposed.Without relying on any line search condition,the search direction generated by the new method always satisfies the sufficient descent condition.Under the strong Wolfe line search condition,the method is strongly convergent for uniformly convex functions and globally convergent for general nonconvex functions.Numerical results show that the hybrid DL-type conjugate gradient method is effective and can successfully restore the image polluted by salt-and-pepper noise.(2)Based on the research framework of the spectral conjugate gradient method,two hybrid spectral conjugate gradient methods with sufficient descent property are proposed.Under the standard Wolfe line search condition,the two methods are globally convergent for general nonconvex functions.Numerical results show that the two new methods have excellent numerical performance and have good application prospects in image restoration.
Keywords/Search Tags:Unconstrained optimization, Dai-Liao type methods, Sufficient descent property, Global convergence, Image restoration
PDF Full Text Request
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