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A nonmonotone Levenberg-Marquardt method for nonlinear complementarity problems under local error bound. (English) Zbl 1359.65093
Summary: 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.

##### MSC:
 65K05 Numerical mathematical programming methods 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
MCPLIB; minpack
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