Adaptive nonmonotone line search method for unconstrained optimization

作者：Zhou Qunyan; Sun Wenyu^*

来源：Frontiers of Mathematics in China, 2008, 3(1): 133-148.

DOI：10.1007/s11464-008-0001-5

• Nonmonotone method
• Newton-type direction
• direction of negative curvature
• adaptive line search
• unconstrained optimization

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.

• 出版日期2008-2
• 单位南京师范大学; 江苏理工学院