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Global Convergence Of Two Classes Of Modified Conjugate Gradient Methods

Posted on:2013-02-04Degree:MasterType:Thesis
Country:ChinaCandidate:P HuFull Text:PDF
GTID:2210330374961529Subject:Operational Research and Cybernetics
Abstract/Summary:PDF Full Text Request
In the methods for solving large-scale unconstrained optimization, theadvantages of conjugate gradient method is simple,easy to program,small to storagecompared with Newton method and Quasi-Newton method. So the conjugategradient method is an important method for solving large-scale unconstrainedoptimization.In this paper, two types of modified conjugate gradient method is given out.The first kind of method is taking example by the correct form of HS method givenby Wei zengxin etc. for modifing the LS method, and combining the modified LS ofconjugate gradient method with the spectrum conjugate gradient method, get amodified spectrum LS conjugate gradient method. The method always producingdrop direction without the dependent of line search conditions, the globalconvergence of the method with the standard Armijo inexact line search,theArmijo-type line search and the Armijo-Goldstein inexact line search is proved, it iseasy to deduce the method also satisfing the global convergence under theArmijo-Goldstein inexact line search rule, finally The given numerical results showthat the modified spectrum LS method is a little better than LS conjugate gradientmethod.The numerical expression of HS method is good, but in the practical calculationoperation, the denominator of βkHSkcould be close to zero, which affect the globalconvergence of the algorithm. The modified HS method given in [34] effectivelysolved this problem. This paper, the second method use the correction method of theliterature [34] to the hybrid conjugate gradient method given by the literature [37],puts forward a modified hybrid conjugate gradient method. The new method havedropped properties under Wolfe line search or the objective function f (x)is strictlyconvex or the parameter1.The global convergence of the new method with Wolfeline search is proved. The numerical experiments are given in the end, the givennumerical result show that the modified hybrid conjugate gradient method is a little better.
Keywords/Search Tags:inexact line search, conjugate gradient method, spectral conjugategradient method, hybrid conjugate gradient method, global convergence
PDF Full Text Request
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