Convergence of DFP Algorithms without Convexity and Exact Line Search Assumptions

Abstract:

In this paper, the convergence of the Broyden algorithms without convexity and exact line search assumptions is discussed. It is proved that if the objective function is suitably smooth and the DFP algorithm produces a convergence point sequence, then the limit point of the sequence is a critical point of the objective function. We give mainly a proof for the DFP update, then point out that all the results are true for Broyden algorithms by a remark.