Sheena, Short answer: Both numbers are informative, but the precise answer depends on what you mean by "iteration." For the PS, it's fine if you give either number as long as you say what it means. Long answer: The number under "function" gives the number of times that the algorithm actually evaluates f(x) before it declares convergence/failure. The number under "counts" gives the number times of times the algorithm evaluates the gradient f'(x) before it declares convergence/failure. Notice that optim BFGS uses a slightly more complicated NR algorithm that separates the step length (ie. how far you walk) and direction (which direction you want to walk). Bluntly speaking, in each full "iteration" the algorithm finds the direction f'(x) (by building a finite-difference approximation of the gradient) and then conditional on that direction it looks for an optimal step length via a bi-section like method by repeatedly calling f(x) looking for the step length that maximizes f(x) in the given direction. Then it takes the step and the procedure is repeated. So in that sense the number of "counts" gives the number of full iterations (ie. including the choice of direction and step length). But the number under "function" tells you of often f(x) was called overall. (Both numbers exclude calls needed to compute the Hessian, if requested, and any calls to compute the finite-difference approximation to the gradient.) Hope this helps. Jens The question was mean to This is a subtle point and the answer In principle the number under "function" A two-element integer vector giving the number of calls to fn and gr respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.