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New properties of a nonlinear conjugate gradient method

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Summary.

This paper provides several new properties of the nonlinear conjugate gradient method in [5]. Firstly, the method is proved to have a certain self-adjusting property that is independent of the line search and the function convexity. Secondly, under mild assumptions on the objective function, the method is shown to be globally convergent with a variety of line searches. Thirdly, we find that instead of the negative gradient direction, the search direction defined by the nonlinear conjugate gradient method in [5] can be used to restart any optimization method while guaranteeing the global convergence of the method. Some numerical results are also presented.

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Received March 12, 1999 / Revised version received April 25, 2000 / Published online February 5, 2001

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Dai, YH. New properties of a nonlinear conjugate gradient method. Numer. Math. 89, 83–98 (2001). https://doi.org/10.1007/PL00005464

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  • DOI: https://doi.org/10.1007/PL00005464

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