New properties of a nonlinear conjugate gradient method. (English) Zbl 1006.65063

This paper provides several new properties of the nonlinear conjugate gradient method in by Y. H. Dai and Y. Yuan [SIAM J. Optim. 10, No. 1, 177-182 (1999; Zbl 0957.65061)]. 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 fine searches. Thirdly, the author finds that instead of the negative gradient direction, the search direction defined by the nonlinear conjugate gradient method of Dai and Yuan [loc. cit.] can be used to restart any optimization method while guaranteeing the global convergence of the method. Some numerical results are also presented.


65K05 Numerical mathematical programming methods
90C52 Methods of reduced gradient type
90C30 Nonlinear programming


Zbl 0957.65061
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