so, hopefully, the sequence (\mathbf{x}_n) converges to the desired local minimum. Note that the value of the step size \gamma is allowed to change at every iteration. With certain assumptions on the function F (for example, F convex and \nabla F Lipschitz) and particular choices of \gamma (e.g., chosen either via a line search that satisfies the Wolfe conditions, or the Barzilai-Borwein method shown as following),
