Global convergence of a class of collinear scaling algorithms with inexact line searches on convex functions (Q1818416)

The first author [Math. Program, Ser. A 49, No. 1, 23-48 (1990; Zbl 0724.90059)] has developed a class of collinear scaling algorithms for unconstrained minimization problems. Some of this algorithms may be considered as an extension of quasi-Newton methods with the Broyden family of approximants of the objective function Hessian. In the present paper, an analogue of the result of \textit{R. H. Byrd}, \textit{J. Nocedal} and \textit{Y. Yuan} [SIAM J. Numer. Anal. 24, 1171-1190 (1987; Zbl 0657.65083)] is proved for the family of collinear scaling algorithms with the line search termination criteria of the first author [loc. cit.]. No numerical tests are given.