Efficient generalized conjugate gradient algorithms, Part 1: theory
Journal of Optimization Theory and Applications
CUTE: constrained and unconstrained testing environment
ACM Transactions on Mathematical Software (TOMS)
A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property
SIAM Journal on Optimization
A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search
SIAM Journal on Optimization
Algorithm 851: CG_DESCENT, a conjugate gradient method with guaranteed descent
ACM Transactions on Mathematical Software (TOMS)
Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization
Optimization Methods & Software
Another nonlinear conjugate gradient algorithm for unconstrained optimization
Optimization Methods & Software
Journal of Computational and Applied Mathematics
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A class of new spectral conjugate gradient methods are proposed in this paper. First, we modify the spectral Perry's conjugate gradient method, which is the best spectral conjugate gradient algorithm SCG by Birgin and Martinez [E.G. Birgin and J.M. Martinez, A spectral conjugate gradient method for unconstrained optimization, Appl. Math. Optim. 43 (2001), 117-128.], such that it possesses sufficient descent property for any (inexact) line search. It is shown that, for strongly convex functions, the method is a global convergent. Further, a global convergence result for nonconvex minimization is established when the line search fulfils the Wolfe line search conditions. Some other spectral conjugate gradient methods with guaranteed descent are presented here. Numerical comparisons are given with both SCG and CG_DESCENT methods using the unconstrained optimization problems in the CUTE library.