In this paper, we introduce a reweighted \(\ell _1\) -penalty method for solving the nonlinear complementarity problem. The novel method not only keeps the semismooth property of the classical \(\ell _1\) -penalty method, but also it has the advantage of the exponential rate of convergence. Specifically, under mild conditions, we prove that there exists some iterative sequence converging to a solution of the original problem with an exponential rate of convergence. Moreover, the semismooth Newton method can be used to efficiently solve the reweighted \(\ell _1\) -penalized equations. Finally, we carry out numerical experiments on test problems from MCPLIB and infinite-dimensional optimization problems. Numerical results show that the proposed method can solve these problems with fewer function evaluations than that of some existing numerical methods.
