An Iterative Method for Finding Stationary Values of a Function of Several Variables

Eighteen months ago Rosenbrock (1960) published a paper in this journal on finding the greatest or least value of a function of several variables. A number of methods were listed and they all have first-order convergence. Six months ago Martin and Tee (1961) published a paper in which they mentioned gradient methods which have second-order convergence for finding the minimum of a quadratic positive definite function. In this paper will be described an iterative method which is not unlike the conjugate gradient method of Hestenes and Stiefel (1952), and which finds stationary values of a general function. It has second-order convergence, so near a stationary value it converges more quickly than Rosenbrock's variation of the steepest descents method and, although each iteration is rather longer because the method is applicable to a general function, the rate of convergence is comparable to that of the more powerful of the gradient methods described by Martin and Tee.