Performance evaluation of a conjugate gradient method considering step length computation techniques in geometry fitting of coordinate measuring machine data

Abstract

This paper focuses on performance evaluation of Hestenes–Stiefel conjugate gradient (CG) method along with two well-known line search conditions, which are weak Wolfe conditions (WWC) and strong Wolfe conditions (SWC), and a new step length computation algorithm in geometry fitting of five primitive geometries (i.e., circle, square, equilateral triangle, ellipse and rectangle). A coordinate measuring machine (CMM) is used to acquire 2D profiles of these geometries. Total number of function evaluations, when the CG method-step length computation technique combination being used successfully completes the geometry fitting, are considered to be performance criteria of the combination. It has been seen that the step length computation techniques for the line search crucially affect the success and performance of the Hestenes–Stiefel CG method in the geometry fitting. Therefore, they require a special care for optimal computational efficiency in addition to the line search direction.