An active-set Levenberg–Marquardt method for degenerate nonlinear complementarity problem under local error bound conditions

摘要

In this paper, we focus on the identification of the degenerate indices of the nonlinear complementarity problem under the local error bound condition. Under this condition, the complementarity problemsmay fail to have non-singularity or local uniqueness at its solutions. We present an active-set Levenberg–Marquardt method, which introduces an estimated set to approximate the degenerate indices of the solutions. When near the solution, the degenerate indices will be correctly identified and the original problem will be transformed to a reduced problem. This method has global convergence. Under the local error bound condition, local superlinear convergence is obtained as well.