A note on the equivalence of a class of factorized Broyden families for nonlinear least squares problems

✍ Scribed by Hideho Ogasawara

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 74 KB
• Volume: 297
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00145-7

✦ Synopsis

This note is concerned with the recently proposed two factorized quasi-Newton updates for solving nonlinear least squares problems. One is a class of updates proposed by Yabe and Yamaki (SIAM Journal on Optimization 5 (1995) 770-791), which was designed as a factorized version of the structured Broyden family with a nonnegative parameter. The other is a class of updates of Xu, Ma and Kong (Journal of Computational Mathematics 14 (1996) 143-158) which was derived as a class of updates satisfying the secant condition in factorized form. It is shown that these classes of updates are essentially the same.