Yin, Zhang; Tewarson, R. P. Least-change updates to Cholesky factors subject to the nonlinear quasi- Newton condition. (English) Zbl 0636.65061 IMA J. Numer. Anal. 7, 509-521 (1987). The authors investigate the derivation of least-change updates [cf. J. E. Dennis jun. and R. B. Schnabel, SIAM Rev. 21, 443-459 (1979; Zbl 0424.65020)] to the Cholesky factors of approximate Hessian matrices in quasi-Newton methods for unconstrained optimization. By considering a variational problem in the weighted Frobenius norm, they obtain explicit formulae for the least-change updates. Reviewer: J.Parida Cited in 3 Documents MSC: 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming Keywords:least-change updates; Cholesky factors; Hessian matrices; quasi-Newton methods; unconstrained optimization; Frobenius norm PDF BibTeX XML Cite \textit{Z. Yin} and \textit{R. P. Tewarson}, IMA J. Numer. Anal. 7, 509--521 (1987; Zbl 0636.65061) Full Text: DOI