The Jacobian consistency of a smoothed Fischer–Burmeister function associated with second-order cones

This paper deals with the second-order cone complementarity problem (SOCCP), which is an important class of problems containing various optimization problems. The SOCCP can be reformulated as a system of nonsmooth equations. For solving this system of nonsmooth equations, smoothing Newton methods are widely used. The Jacobian consistency property plays an important role for achieving a rapid convergence of the methods. In this paper, we show the Jacobian consistency of a smoothed Fischer–Burmeister function. Moreover, we estimate the distance between the subgradient of the Fischer–Burmeister function and the gradient of its smoothing function.