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This paper examines the numerical performances of two methods for large-scale optimization: a limited memory quasi-Newton method (L-BFGS), and a discrete truncated-Newton method (TN). Various ways of classifying test problems are discussed in order to better understand the types of problems that each algorithm solves well. The L-BFGS and TN methods are also compared with the Polak–Ribiere conjugate gradient method.

A Numerical Study of the Limited Memory BFGS Method and the Truncated-Newton Method for Large Scale Optimization