A Smoothing Method with Appropriate Parameter Control Based on Fischer-Burmeister Function for Second-Order Cone Complementarity Problems

Abstract EN

We deal with complementarity problems over second-order cones.

The complementarity problem is an important class of problems in the real world and involves many optimization problems.

The complementarity problem can be reformulated as a nonsmooth system of equations.

Based on the smoothed Fischer-Burmeister function, we construct a smoothing Newton method for solving such a nonsmooth system.

The proposed method controls a smoothing parameter appropriately.

We show the global and quadratic convergence of the method.

Finally, some numerical results are given.