Open AccessGlobal convergence of a modified Broyden family method for nonconvex functions
Author(s) -
Gonglin Yuan,
Zhan Wang,
Pengyuan Li
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021164
Subject(s) - broyden–fletcher–goldfarb–shanno algorithm , mathematics , line search , convergence (economics) , sequence (biology) , positive definiteness , algorithm , computer science , positive definite matrix , computer network , computer security , asynchronous communication , biology , economics , radius , genetics , economic growth , eigenvalues and eigenvectors , physics , quantum mechanics
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 \begin{document}$ \{B_k\} $\end{document} 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.