Adaptive nonmonotone line search method for unconstrained optimization

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  • 1.School of Mathematics and Computer Science, Nanjing Normal University;Department of Basic Science, Jiangsu Teacher University of Technology; 2.School of Mathematics and Computer Science, Nanjing Normal University;

Published date: 05 Mar 2008

Abstract

In this paper, an adaptive nonmonotone line search method for unconstrained minimization problems is proposed. At every iteration, the new algorithm selects only one of the two directions: a Newton-type direction and a negative curvature direction, to perform the line search. The nonmonotone technique is included in the backtracking line search when the Newton-type direction is the search direction. Furthermore, if the negative curvature direction is the search direction, we increase the steplength under certain conditions. The global convergence to a stationary point with second-order optimality conditions is established. Some numerical results which show the efficiency of the new algorithm are reported.

Cite this article

ZHOU Qunyan, SUN Wenyu . Adaptive nonmonotone line search method for unconstrained optimization[J]. Frontiers of Mathematics in China, 2008 , 3(1) : 133 -148 . DOI: 10.1007/s11464-008-0001-5

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