An iterative method for a system of linear complementarity problems with perturbations and interval data

In this paper, we introduce a total step method for solving a system of linear complementarity problems with perturbations and interval data. It is applied to two interval matrices [A] and [B] and two interval vectors [b] and [c]. We prove that the sequence generated by the total step method converges to ([x∗],[y∗]) which includes the solution set for the system of linear complementarity problems defined by any fixed A∈[A],B∈[B],b∈[b] and c∈[c]. We also consider a modification of the method and show that, if we start with two interval vectors containing the limits, then the iterates contain the limits. We close our paper with two examples which illustrate our theoretical results.