Primal-dual Interior Point Algorithms for LCPs with Arbitrary Matrices

We have generalized some interior point algorithms (IPA) to solve LCPs in the sense of the EP-theorem. These algorithms stop in polynomial time with one of the following: (i) a solution for LCP is obtained, (ii) a solution for dual LCP is obtained, (iii) the matrix of the problem is not in the class of P*(k)-matrices for an a priori given k. The practical applicability of our algorithms will be illustrated on the Arrow-Debreu exchange market model, that was reformulated as an LCP by Ye.