A tool for the analysis of Quasi-Newton methods with application to unconstrained minimization
SIAM Journal on Numerical Analysis
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
CUTE: constrained and unconstrained testing environment
ACM Transactions on Mathematical Software (TOMS)
A survey of truncated-Newton methods
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
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
Convergence Properties of the BFGS Algoritm
SIAM Journal on Optimization
The Superlinear Convergence of a Modified BFGS-Type Method for Unconstrained Optimization
Computational Optimization and Applications
A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search
SIAM Journal on Optimization
Notes on the Dai-Yuan-Yuan modified spectral gradient method
Journal of Computational and Applied Mathematics
A modified Polak-Ribière-Polyak conjugate gradient algorithm for nonsmooth convex programs
Journal of Computational and Applied Mathematics
A regularized limited memory BFGS method for nonconvex unconstrained minimization
Numerical Algorithms
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In this paper, a new numerical method for solving large-scale unconstrained optimization problems is presented. It is derived from a modified BFGS-type update formula by Wei, Li, and Qi. It is observed that the update formula can be extended to the framework of limited memory scheme with hardly more storage or arithmetic operations. Under some suitable conditions, the global convergence property is established. The implementations of the method on a set of CUTE problems indicate that this extension is beneficial to the performance of the algorithm.