Circuit design by minimization using the Hessian matrix

The Hessian matrix of the objective function in the problem of circuit design by minimization can be determined explicitly and its use in a second-order minimization process is now feasible and is presented. The process begins with the steepest descent method, followed by a generalized Newton method. At each iteration, the incremental step as prescribed by the respective method is taken unless the function is locally increasing, in which case, the direction is reversed. If the function has increased at a trial point, a cubic interpolation between the current point and that point is performed and the next point is taken to be at the minimum of the cubic. To ensure that the cubic approximation is reasonable, the step size is controlled. Examples are given and the results are compared with those obtained by the gradient method of Fletcher and Powell.