Global convergence of a nonmonotone Broyden family method for nonconvex unconstrained minimization

In this paper, a nonmonotone Broyden family method is presented for the unconstrained optimization problems. The proposed line search technique is designed based on a nonmonotone line search proposed by Huang, Wan and Zhang (J. Comput. Appl. Math. 330: 586-604, 2018). The new line search technique can overcome the shortcoming that the nonmonotone line search proposed by Huang et. al only can be applied to conjugate gradient (CG) method, not Broyden family (including BFGS-type) method. The proposed method in this paper possesses some good properties: (i) a new nonmonotone line search technique is presented, (ii) the proposed nonmonotone line search technique can be applied not only to CG method but also to Broyden family (including BFGS-type) method, (iii) global convergence of the Broyden family method has been obtained with the proposed nonmonotone line search for nonconvex unconstrained minimization. In addition, numerical performance shows that the nonmonotone Broyden family method is more competitive versus the classical Broyden family method.

Automated summary

This paper presents a nonmonotone Broyden family method for unconstrained optimization problems, which possesses global convergence and better performance.