A full-Newton step infeasible interior-point algorithm for P*(κ) linear complementarity problem

This paper proposes a new infeasible interior-point algorithm with full-Newton steps for P*(κ) linear complementarity problem (LCP), which is an extension of the work by Roos (SIAM J. Optim., 2006, 16(4): 1110–1136). The main iteration consists of a feasibility step and several centrality steps. The authors introduce a specific kernel function instead of the classic logarithmical barrier function to induce the feasibility step, so the analysis of the feasibility step is different from that of Roos’s. This kernel function has a finite value on the boundary. The result of iteration complexity coincides with the currently known best one for infeasible interior-point methods for P*(κ) LCP. Some numerical results are reported as well.