This paper applies a convex combination non-monotone Wolfe line-search proposed recently to the convergence analysis of Broyden’s family quasi-Newton method.We show that under the convex combination non-monotone Wolfe line-search

a modified Broyden’s non-convex family take on global and superlinear convergence.The results extend line-search condition for the convergence analysis of the modified Broyden’s non-convex family.Finally

primary numerical results are presented.Numerical results show that the computation efficiency of the modified Broyden’s non-convex family under the convex combination non-monotone Wolfe line-search is superior to that under monotone Wolfe line-search.