A nonmonotone Levenberg-Marquardt method for nonlinear complementarity problems under local error bound

作者：Fan, Bin^*

来源：COMPUTATIONAL & APPLIED MATHEMATICS, 2017, 36(1): 185-202.

DOI：10.1007/s40314-015-0222-7

• Nonlinear complementarity problems
• Nonsmooth equations
• Nonmonotone Levenberg-Marquardt algorithm
• Global convergence
• Superlinear/quadratic convergence

In this paper, we propose a new Levenberg-Marquardt algorithm for nonlinear complementarity problems. The algorithm is based on a semismooth equation reformulation of the complementarity problem using the FB function. To obtain the global convergence, we use a modified nonmonotone line search rule. Under the local error bound assumption, which is weaker than the nonsingularity condition, we get the local superlinear/quadratic convergence of the algorithm. Some numerical examples are given to illustrate the performance and efficiency of the presented algorithm.

• 出版日期2017-3
• 单位福建师范大学