Verification for existence of solutions of linear complementarity problems

Recently, G. Alefeld, X. Chen and F. Potra [Numer. Math. 83 (1999) 265-315] presented a verification method for solutions of linear complementarity problems (LCPs). This paper is an attempt to obtain more useful information from the output of this verification method. In particular, existing results can only claim the nonexistence of solutions in a given interval. We will use the Farkas lemma to check if the interval contains a negative certification which shows the nonexistence of solutions in the whole space Rn. Moreover, we will study how to choose a good nonsingular matrix A in the interval operator for P0-matrix linear complementarity problems. We report numerical results to illustrate the efficiency of the proposed technique.