Complementarity Functions and Numerical Experiments on Some Smoothing Newton Methods for Second-Order-Cone Complementarity Problems

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Two results on the second-order-cone complementarity problem are presented. We show that the squared smoothing function is strongly semismooth. Under monotonicity and strict feasibility we provide a new proof, based on a penalized natural complementarity function, for the solution set of the second-order-cone complementarity problem being bounded. Numerical results of squared smoothing Newton algorithms are reported.