Generalized Second-Order Complementarity Problems: Theory and Numerical Experiments

The generalized second-order cone complementarity problem (GSOCCP) is reformulated via bound-constrained minimization, preserving differentiability of the original data. Four reformulations are proposed, which are tested in five low dimensional instances. A thorough presentation and discussion of the numerical experiments is provided, to illustrate the performance of the reformulations. In a companion paper, equivalence results relating global minimizers of two of the reformulations with zero objective function value and solutions to GSOCCP are proved, together with sufficient conditions for ensuring correspondence between stationary points of one of the reformulations and solutions to GSOCCP. Reference to these results are included, with additional theoretical insight into the second reformulation that has beenpreviously addressed.