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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.
MSC:
65K05Mathematical programming (numerical methods)
90C52Methods of reduced gradient type
90C30Nonlinear programming