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Two Modified Polak–Ribière–Polyak-Type Nonlinear Conjugate Methods with Sufficient Descent Property
Authors:Zhifeng Dai
Institution:1. College of Mathematics and Computational Science , Changsha University of Science and Technology , Changsha, P. R. China zhifengdai823@163.com
Abstract:In this article, we propose a new conjugate gradient type formula for computing unconstrained optimization problems. Its form is similar to the original PRP formula and it inherits all nice properties of the PRP method. By utilizing the technique of the three-term PRP method in Zhang 20 L. Zhang , W.J. Zhou , and D.H. Li ( 2006 ). A descent modified Polak-Ribiére-Polyak conjugate gradient method and its global convergence . IMA J. Numer. Anal. 26 : 629640 .Crossref], Web of Science ®] Google Scholar]] and modified PRP method in Yu 17 G.H. Yu ( 2007 ). Nonlinear self-scaling conjugate gradient methods for large-scale optimization problems. Thesis of Doctors Degree, Sun Yat-Sen University . Google Scholar]], we propose two modified methods of the new formula. The two modified methods all can generate sufficient descent directions which is independent of the line search used. Under some mild conditions, the global convergence and the linearly convergent rate of the two modified methods are established. The numerical results show that the proposed methods are efficient.
Keywords:Conjugate gradient method  Global convergence  R-linear convergence  Sufficient descent property  Unconstrained optimization
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