A Smoothing Newton Method with Fischer‐Burmeister Function for Second‐Order Cone Complementarity Problems

The second-order cone complementarity problem (SOCCP) is an important class of problems containing a lot of optimization problems. The SOCCP can be transformed into a system of nonsmooth equations. To solve this nonsmooth system, smoothing techniques are often used. Fukushima, Luo and Tseng (2001) studied concrete theories and properties of smoothing functions for the SOCCP. Recently, a practical computational method using the smoothed natural residual function to solve the SOCCP was given by Chen, Sun and Sun (2003). In the present paper, we propose an algorithm to solve the SOCCP by using the smoothed Fischer-Burmeister function. Some preliminary numerical results are given.