The convergence of quasi-Newton matrices generated by the self-scaling symmetric rank one update (Q1267799)

Quasi-Newton algorithms for unconstrained optimization generate a sequence of matrices that can be considered as approximations to the objective function second derivatives. This paper gives some conditions under which the approximations generated by the self-scaling symmetric rank one update formula [\textit{L. P. Sun}, J. Comput. Math. Chinese Univ. 3, 15-25 (1984)] can be proved to converge globally to the true correct Hessian matrix. The theory is confirmed by preliminary numerical tests.