The authors extend the line search termination criterion for collinear scaling algorithms of K. A. Ariyawansa [Numer. Math. 80, No. 3, 363-376 (1998; Zbl 0916.65061)] for minimization problems \[ \underset{x\in X}{\text{minimum}} f(x), \] where \(f: x\to\mathbb{R}\) is continuous and \(X\subseteq \mathbb{R}^n\) is open. It is shown that the criterion of Ariyawansa is successful in handling a much larger class of functions, including convex and strictly pseudo-convex functions. An example is presented.