An Eigenvalue Study on the Sufficient Descent Property of a Modified Polak-ribi Ere-polyak Conjugate Gradient Method
نویسنده
چکیده
Based on an eigenvalue analysis, a new proof for the sufficient descent property of the modified Polak-Ribière-Polyak conjugate gradient method proposed by Yu et al. is presented.
منابع مشابه
An eigenvalue study on the sufficient descent property of a modified Polak-Ribière-Polyak conjugate gradient method
Based on an eigenvalue analysis, a new proof for the sufficient descent property of the modified Polak-Ribière-Polyak conjugate gradient method proposed by Yu et al. is presented.
متن کاملExtensions of the Hestenes-Stiefel and Polak-Ribiere-Polyak conjugate gradient methods with sufficient descent property
Using search directions of a recent class of three--term conjugate gradient methods, modified versions of the Hestenes-Stiefel and Polak-Ribiere-Polyak methods are proposed which satisfy the sufficient descent condition. The methods are shown to be globally convergent when the line search fulfills the (strong) Wolfe conditions. Numerical experiments are done on a set of CUTEr unconstrained opti...
متن کاملA descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence
In this paper, we propose a modified Polak–Ribière–Polyak (PRP) conjugate gradient method. An attractive property of the proposed method is that the direction generated by the method is always a descent direction for the objective function. This property is independent of the line search used. Moreover, if exact line search is used, the method reduces to the ordinary PRP method. Under appropria...
متن کاملConvergence Properties of Nonlinear Conjugategradient
Recently, important contributions on convergence studies of conjugate gradient methods have been made by Gilbert and Nocedal 6]. They introduce a \suucient descent condition" to establish global convergence results, whereas this condition is not needed in the convergence analyses of Newton and quasi-Newton methods, 6] hints that the suucient descent condition, which was enforced by their two-st...
متن کاملA New Hybrid Conjugate Gradient Method Based on Eigenvalue Analysis for Unconstrained Optimization Problems
In this paper, two extended three-term conjugate gradient methods based on the Liu-Storey ({tt LS}) conjugate gradient method are presented to solve unconstrained optimization problems. A remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition independent of line search method, based on eigenvalue analysis. The globa...
متن کامل