A Levenberg-Marquardt Method for Nonlinear Complementarity Problems Based on Nonmonotone Trust Region and Line Search Techniques

作者：Fan, Bin^*; Ma, Changfeng; Wu, Aidi; Wu, Chao

来源：Mediterranean Journal of Mathematics, 2018, 15(3): 118.

DOI：10.1007/s00009-018-1168-y

• Nonlinear complementarity problems
• nonmonotone Levenberg-Marquardt algorithm
• trust region technique
• global convergence
• superlinear/quadratic convergence

Using the FB function, we propose a new Levenberg-Marquardt algorithm for nonlinear complementarity problem. To obtain the global convergence, the algorithm uses the nonmonotone trust region and line search techniques under a convenient boundedness assumption. Furthermore, we get local superlinear/quadratic convergence of the algorithm under a nonsingularity condition. Some numerical examples are given to illustrate the performance and efficiency of the presented algorithm.

• 出版日期2018-6
• 单位福建师范大学; 福建农林大学; 厦门大学