A full-modified-Newton step feasible interior-point algorithm for a class of linear weighted complementarity problems

As the extension of a complementarity problem, the weighted complementarity problem is an important kind of equilibrium problem, which could be used to model a larger class of practical equilibrium problems in economy and finance. Because of the nonzero weight vector, the weighted complementarity problem is usually more complicated than the complementarity problem. There is little available work about the algorithms for the weighted complementarity problem. In this paper, an interior-point algorithm is extended from linear optimization to weighted complementarity problems. Based on an equivalent reformulation of central path, a full-modified-Newton step feasible interior-point algorithm is proposed for solving a class of linear weighted complementarity problems over the nonnegative orthant. There is no linear search at each iteration. Under appropriate assumptions, we prove the feasibility of the algorithm, and obtain the iteration complexity. The numerical results illustrate that the algorithm is effective.