Equivalence Between Different Formulations of the Linear Complementarity Problem
Optimization Methods and Software
One shows that different formulations of the linear complementarity problem (LCP), such as the horizontal LCP, the mixed LCP and the geometric LCP can be transformed into a standard LCR The P*(k)-property (a more general property than monotonicity) of the corresponding formulations as well as the convergence properties of a large class of interior-point algorithms are invariant with respect to the transformations. Therefore it is sufficient to study the algorithms only for the standard LCP
Anitescu, Mihai, Goran Lesaja, Florian A. Potra.
"Equivalence Between Different Formulations of the Linear Complementarity Problem."
Optimization Methods and Software, 7 (3-4): 265-290.
doi: 10.1080/10556789708805657 source: https://www.tandfonline.com/doi/abs/10.1080/10556789708805657