Global convergence of a modified Broyden family method for nonconvex functions
release_qdwnfo5yszccxn2xp4ajfx7say
by
Gonglin Yuan, Zhan Wang, Pengyuan Li
2021
Abstract
<jats:p xml:lang="fr"><p style='text-indent:20px;'>The Broyden family method is one of the most effective methods for solving unconstrained optimization problems. However, the study of the global convergence of the Broyden family method is not sufficient. In this paper, a new Broyden family method is proposed based on the BFGS formula of Yuan and Wei (Comput. Optim. Appl. 47: 237-255, 2010). The following approaches are used in the designed algorithm: (1) a modified Broyden family formula is given, (2) every matrix sequence <inline-formula><tex-math id="M1">\begin{document}$ \{B_k\} $\end{document}</tex-math></inline-formula> generated by the new algorithm possesses positive-definiteness, and (3) the global convergence of the new presented Broyden family algorithm with the Y-W-L inexact line search is obtained for general functions. Numerical performance shows that the modified Broyden family method is competitive with the classical Broyden family method.
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