Smoothing Levenberg–Marquardt method for general nonlinear complementarity problems under local error bound

Abstract

By using the F–B function and smoothing technique to convert the nonlinear complementarity problems to smoothing nonlinear systems, and introducing perturbation parameter μ k into the smoothing Newton equation, we present a new smoothing Levenberg–Marquardt method for general nonlinear complementarity problems. For general mapping F, not necessarily a P 0 function, the algorithm has global convergence. Each accumulation point of the iterative sequence is at least a stationary point of the problem. Under the local error bound condition, which is much weaker than nonsingularity assumption or the strictly complementarity condition, we get the local superlinear convergence. Under some proper condition, quadratic convergence is also obtained.