An extension of the potential reduction algorithm for linear complementarity problems with some priority goals

Abstract We extend the potential reduction algorithm to solve the restricted convex linear complementarity problem (LCP) x T s =0, x I =0, s J =0, s = Mx + q , and 0⩽ x , s ϵ R n for some index sets I and J . In polynomial time, the algorithm will either discover that no solution exists or generate a sequence of pairs ( x k , s k which simultaneously drives ( x k ) T s k , x k I , and s k J to zero. In particular, we discuss how to apply the algorithm to solving the combined Phase I–Phase II convex LCP and to identifying a vertex linear programming solution.