The revised DFP algorithm without exact line search

Authors:
Dingguo Pu;Weiwen Tian
Affiliations:
Department of Applied Mathematics, Tongji University, 1239 Siping Road, Shanghai, 200092, China;Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200436, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

In this paper, we discuss the convergence of the DFP algorithm with revised search direction. Under some inexact line searches, we prove that the algorithm is globally convergent for continuously differentiable functions and the rate of convergence of the algorithm is one-step superlinear and n-step second order for uniformly convex objective functions.From the proof of this paper, we obtain the superlinear and n-step second-order convergence of the DFP algorithm for uniformly convex objective functions.