New smooth weighted complementarity functions and a cubically convergent method for wLCP

The weighted linear complementarity problem (wLCP) can be used for modelling a large class of problems from science and economics. In this paper, we introduce a new class of weighted complementarity functions and show that it is continuously differentiable everywhere. By using this function, we propose a two steps Levenberg–Marquardt-type method to solve the wLCP. Under suitable conditions, we prove that the proposed method is globally convergent and the generated iteration sequence is bounded. Moreover, we show that the proposed method has cubic convergence rate under the local error bound condition. Some numerical results are reported.