A smoothing Newton method based on the generalized Fischer–Burmeister function for MCPs

We present a smooth approximation for the generalized Fischer–Burmeister function where the 2-norm in the FB function is relaxed to a general pp-norm (p>1p>1), and establish some favorable properties for it — for example, the Jacobian consistency. With the smoothing function, we transform the mixed complementarity problem (MCP) into solving a sequence of smooth system of equations, and then trace a smooth path generated by the smoothing algorithm proposed by Chen (2000) [28] to the solution set. In particular, we investigate the influence of pp on the numerical performance of the algorithm by solving all MCPLIP test problems, and conclude that the smoothing algorithm with p∈(1,2]p∈(1,2] has better numerical performance than the one with p>2p>2.