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On the convergence property of the DFP algorithm

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Abstract

The DFP algorithm of unconstrained optimization possesses excellent properties of convergence for convex functions. However, a convergence theory of the DFP algorithm without the convexity assumption has not yet been established. This paper gives the following result: If the objective function is suitably smooth, and if the DFP algorithm produces a convergent point sequence, then the limit point of the sequence is a critical point of the objective function. Also, some open questions are mentioned.

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Authors and Affiliations

  1. Mathematics Division, Railway Institute of Shanghai, 200333, Shanghai, P.R. China

    Dingguo Pu

  2. Applied Mathematics Institute, East China University of Chemical Technology, 200433, Shanghai, P.R. China

    Wenci Yu

Authors
  1. Dingguo Pu
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  2. Wenci Yu
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Supported by the National Science Foundation of China.

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Pu, D., Yu, W. On the convergence property of the DFP algorithm. Ann Oper Res 24, 175–184 (1990). https://doi.org/10.1007/BF02216822

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  • DOI: https://doi.org/10.1007/BF02216822

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