This article presents a reformulation of the generalized complementarity problem over a polyhedral cone. The authors re-formulate the problem as a constrained programming problem based on the Fisher function from \(\mathbb R^2\) to \(\mathbb R\), and is then optimized using a Newton-type algorithm. It is further shown that, under certain conditions, the algorithm converges globally and quadratically. The article concludes with a section on computational experimentation.