Convergence of nonmonotone line search method

Authors:
Zhen-Jun Shi;Jie Shen
Affiliations:
Col. of Ops. Res. and Mgmt., Qufu Normal Univ., Rizhao, Shandong, PR China and Inst. of Computl. Math. and Sci./Eng. Comp., Acad. of Math. and Sys. Sci., Ch. Acad. of Sci., Beifing, PR China;Department of Computer and Information Science, University of Michigan, Dearborn, MI
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

In this paper, we develop a new nonmonotone line search for general line search method and establish some global convergence theorems. The new nonmonotone line search is a novel form of the nonmonotone Armijo line search and allows one to choose a larger step size at each iteration, which is available in constructing new line search methods and possibly reduces the function evaluations at each iteration. Moreover, we analyze the convergence rate of some special line search methods with the new line search. Preliminary numerical results show that some line search methods with the new nonmonotone line search are available and efficient in practical computation.