Abstract
In this paper, a new modified BFGS method without line searches is proposed. Unlike traditional BFGS method, this modified BFGS method is proposed based on the so-called fixed steplength strategy introduced by Sun and Zhang. Under some suitable assumptions, the global convergence and the superlinear convergence of the new algorithm are established, respectively. And some preliminary numerical experiments, which shows that the new Algorithm is feasible, is also reported.
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