Academy of Sciences of the Czech Republic Computational experience with modified conjugate gradient methods for unconstrained optimization
نویسندگان
چکیده
In this report, several modifications of the nonlinear conjugate gradient method are described and investigated. Theoretical properties of these modifications are proved and their practical performance is demonstrated using extensive numerical experiments.
منابع مشابه
An Efficient Conjugate Gradient Algorithm for Unconstrained Optimization Problems
In this paper, an efficient conjugate gradient method for unconstrained optimization is introduced. Parameters of the method are obtained by solving an optimization problem, and using a variant of the modified secant condition. The new conjugate gradient parameter benefits from function information as well as gradient information in each iteration. The proposed method has global convergence und...
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 کاملThe modified BFGS method with new secant relation for unconstrained optimization problems
Using Taylor's series we propose a modified secant relation to get a more accurate approximation of the second curvature of the objective function. Then, based on this modified secant relation we present a new BFGS method for solving unconstrained optimization problems. The proposed method make use of both gradient and function values while the usual secant relation uses only gradient values. U...
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 کاملAn 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 کامل