Equivalence between different formulations of the linear complementarity problem

Mihai Anitescu, Lesaja Goran, Florian A. Potra

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 LCP. The $P_*(\k)$-property 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.

Reports on Computational Mathematics, No.71, Department of Mathematics, The University of Iowa, June 1995.