On Davidon's collinear scaling algorithms for optimization (Q1332350)

\textit{W. C. Davidon} [SIAM J. Numer. Anal. 17, 268-281 (1980; Zbl 0424.65026)] presented a new class of algorithms for unconstrained optimization. These algorithms are related to quasi-Newton methods, and are based on local collinear scalings and local conic approximations, which extend local affine scalings and local quadratic approximations used in derivations of quasi-Newton methods. The algorithms of Davidon have not been studied theoretically or computationally. Algorithms based on collinear scalings and conic approximations related to quasi-Newton methods that have been investigated todate are all derived based on an approach by \textit{D. C. Sorensen} [ibid. 17, 84-114 (1980; Zbl 0428.65040)]. In this note, the author shows that all these algorithms derived using the approach of Sorensen are in fact different from the algorithms that Davidon presented.