Evaluation of Step Directions in Optimization Algorithms

We present a method for comparing that part of optimization algorithms that chooses each step direction. It is an example of a general approach to algorithm evaluation in which one tests specific parts of the algorithm, rather than making overall evaluations on a set of standard test problems. Our testing procedure can he useful for developing new algorithms and for writing and evaluating optimization software. We use the method to compare two versions of the conjugate gradient algorithm, and to compare these with an algorithm based on conic functions.