On the convergence property of the DFP algorithm |
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| Authors: | Dingguo Pu Wenci Yu |
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| Institution: | (1) Mathematics Division, Railway Institute of Shanghai, 200333 Shanghai, P.R. China;(2) Applied Mathematics Institute, East China University of Chemical Technology, 200433 Shanghai, P.R. China |
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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.Supported by the National Science Foundation of China. |
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| Keywords: | DFP algorithm unconstrained optimization without convexity convergence |
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