The algorithms presented here can be applied to quadratic and non-quadratic objective functions alike. The term local refers both to the fact that only information about a function from the neighborhood of the current approximation is used in updating the approximation as well as that we usually expect such methods to converge to whatever local extremum is closest to the starting approximation. As a result, the global structure of an objective function is unknown to a local method. Some of these techniques, such as Downhill Simplex and Powell's method do not require the derivatives of the objective function. Others, such as the quasi-Newton methods require at least the gradient. In the latter case, if analytic expressions are not available for the derivatives, a module for finite-difference calculation of the gradient is provided. COOOL also includes nonquadratic generalizations of the conjugate gradient method incorporating two different kind of line search procedures.