Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Line search algorithms with guaranteed sufficient decrease
ACM Transactions on Mathematical Software (TOMS)
CUTE: constrained and unconstrained testing environment
ACM Transactions on Mathematical Software (TOMS)
A globally convergent version of the Polak-Ribière conjugate gradient method
Mathematical Programming: Series A and B
A modified BFGS method and its global convergence in nonconvex minimization
Journal of Computational and Applied Mathematics - Special issue on nonlinear programming and variational inequalities
On the Global Convergence of the BFGS Method for Nonconvex Unconstrained Optimization Problems
SIAM Journal on Optimization
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
A new Liu-Storey type nonlinear conjugate gradient method for unconstrained optimization problems
Journal of Computational and Applied Mathematics
SIAM Journal on Optimization
Journal of Computational and Applied Mathematics
A simple three-term conjugate gradient algorithm for unconstrained optimization
Journal of Computational and Applied Mathematics
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In this paper, we propose a three-term conjugate gradient method which can produce sufficient descent condition, that is, [image omitted] . This property is independent of any line search used. When an exact line search is used, this method reduces to the standard Hestenes-Stiefel conjugate gradient method. We also introduce two variants of the proposed method which still preserve the sufficient descent property, and prove that these two methods converge globally with standard Wolfe line search even if the minimization function is nonconvex. We also report some numerical experiment to show the efficiency of the proposed methods.