Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Some numerical experiments with variable-storage quasi-Newton algorithms
Mathematical Programming: Series A and B
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Representations of quasi-Newton matrices and their use in limited memory methods
Mathematical Programming: Series A and B
BFGS with Update Skipping and Varying Memory
SIAM Journal on Optimization
Shifted limited-memory variable metric methods for large-scale unconstrained optimization
Journal of Computational and Applied Mathematics
Shifted limited-memory variable metric methods for large-scale unconstrained optimization
Journal of Computational and Applied Mathematics
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This paper studies recent modifications of the limited memory BFGS (L-BFGS) method for solving large scale unconstrained optimization problems. Each modification technique attempts to improve the quality of the L-BFGS Hessian by employing (extra) updates in a certain sense. Because at some iterations these updates might be redundant or worsen the quality of this Hessian, this paper proposes an updates criterion to measure this quality. Hence, extra updates are employed only to improve the poor approximation of the L-BFGS Hessian. The presented numerical results illustrate the usefulness of this criterion and show that extra updates improve the performance of the L-BFGS method substantially.