Nonnegative iterative reweighted method for sparse linear complementarity problem

Solution of sparse linear complementarity problem (LCP) has been widely discussed in many applications. In this paper, we consider the ${\ell }_p$ regularization problem with nonnegative constraint for sparse LCP, and propose algorithms based on the iterative reweighted method to approach a sparse solution of the LCP, and then show the convergence to the stationary point of ${\ell }_p$ regularization problem. Numerical results on simulated data exhibit an excellent performance of the proposed algorithms on approaching a sparse solution of the LCP. Finally, we apply this method to the frictional and frictionless contact problems. The numerical experiments demonstrate that the contact problems can be efficiently solved by the proposed algorithm.