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

Dai, Yu-Hong

Numer. Math. 89, No. 1, 83-98 (2001).

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.

Reviewer: Jürgen Guddat (Berlin)

MSC:

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

Keywords:

nonlinear conjugate gradient method; global convergence; numerical results

Citations:

Zbl 0957.65061