This paper continues to address one of its author's obsession with the well- known problem of dealing with non-convexity during the minimization of a nonlinear function f(x) by Newton-like methods. It builds on some proposals made by the present authors in "A Comparison of methods for traversing regions of non-convexity in optimization problems". (Numerical Algorithms (2019)) which involve the use of a search along a curve which approximates the continuous steepest descent path. In this note we consider ways of carrying out this search more economically than in the algorithm as originally proposed and presents some encouraging numerical evidence.
Unpublished report, University of Hertfordshire, Hatfield, England, March 2021