line search methods for unconstrained optimization based on satisfying the wolfe conditions impose a restriction on the value of the directional derivative of the objective function at the new iterate. projected search methods for bound-constrained optimization involve a line search along a continuous piecewise-linear path, which makes it impossible to apply the conventional wolfe conditions. we propose a new quasi-wolfe line search for piecewise differentiable functions. the behavior of the line search is similar to that of a conventional wolfe line search, except that a step is accepted under a wider range of conditions. these conditions take into consideration steps at which the line search function is not differentiable. some basic results associated with a conventional wolfe line search are established for the quasi-wolfe case. after identifying the practical considerations needed for converting a wolfe line search into a quasi-wolfe line search, details of the imp lementation along with some numerical results will be presented.