  The limited memory BFGS (L-BFGS) method is one of the popular methods for
solving large-scale unconstrained optimization. Since the standard L-BFGS
method uses a line search to guarantee its global convergence, it sometimes
requires a large number of function evaluations. To overcome the difficulty, we
propose a new L-BFGS with a certain regularization technique. We show its
global convergence under the usual assumptions. In order to make the method
more robust and efficient, we also extend it with several techniques such as
nonmonotone technique and simultaneous use of the Wolfe line search. Finally,
we present some numerical results for test problems in CUTEst, which show that
the proposed method is robust in terms of solving number of problems.
