A note on “A globally convergent BFGS method with nonmonotone line search for non-convex minimization”

摘要

In this note, we point out that Assumption 3.1, Assumption 3.2 in [Y. Xiao, H. Sun, Z. Wang, A globally convergent BFGS method with nonmonotone line search for non-convex minimization, J. Comput. Appl. Math. 230 (2009) 95–106] are not enough to guarantee the global convergence result Theorem 3.1 in [1]. We present a new assumption and show that the proposed method in [1] still converges globally under these three assumptions.