Unconstrained Minimization Techniques - Steepest Descent Iterations

When initial values for q are far from the ultimate minimum, the approximate Hessian Hk may fail to yield a proper step direction during iteration. In this case, the program may iterate into a region of the parameter space from which recovery (i.e., successful iteration to the true minimum point) is not possible. In such cases, SEPATH offers several options to help control the iteration process. One option is to precede the Gauss-Newton procedure with a few iterations utilizing the "method of steepest descent." In the steepest descent approach, values of q on each iteration are obtained as