Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Convergence Properties of Nonlinear Conjugate Gradient Methods
SIAM Journal on Optimization
Global convergence of a two-parameter family of conjugate gradient methods without line search
Journal of Computational and Applied Mathematics - Special issue: Papers presented at the 1st Sino--Japan optimization meeting, 26-28 October 2000, Hong Kong, China
The Superlinear Convergence of a Modified BFGS-Type Method for Unconstrained Optimization
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
Two new conjugate gradient methods based on modified secant equations
Journal of Computational and Applied Mathematics
Convergence analysis of a modified BFGS method on convex minimizations
Computational Optimization and Applications
Two effective hybrid conjugate gradient algorithms based on modified BFGS updates
Numerical Algorithms
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
A modified Polak-Ribière-Polyak conjugate gradient algorithm for nonsmooth convex programs
Journal of Computational and Applied Mathematics
Two modified scaled nonlinear conjugate gradient methods
Journal of Computational and Applied Mathematics
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The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization due to the simplicity of their iterations and their very low memory requirements. Based on a new quasi-Newton equation proposed in [Z. Wei, G. Li, L. Qi, New quasi-newton methods for unconstrain optimization, preprint, Z. Wei, G. Yu, G. Yuan, Z. Lian, The superlinear convergence of a modified BFGS-type method for unconstrained optimization, Comput. Optim. Appl. 29(3) (2004) 315-332], we establish a new conjugacy condition for CG methods and propose several new CG methods. It is a interesting feature that these new CG methods take both the gradient and function value information. Under some suitable conditions, the global convergence is achieved for these methods. The numerical results show that one of our new CG methods is very encouraging.