we briefly survey line search algorithms for unconstrained optimization. next, we consider the search direction and line search strategies used in several algorithms that implement a quasi-newton method for simple bounds, including algorithm l-bfgs-b. in this context, we discuss two currently-used line search algorithms and introduce a new method meant to combine the best properties of two different strategies. we present a modified l-bfgs-b method using the new line search and demonstrate its significant performance gains by numerical tests using the cuter test set.