On the optimal solution of interval linear complementarity problems

We consider compact intervals [a, a] := {x ∈ IR : a ≤ x ≤ a} and denote the set of all such intervals by IR. We also write [a] instead of [a, a]. Furthermore, we consider matrices with an interval in each of its elements; i.e., [A,A] = ([aij ]) = ([aij , aij ]). We also write [A,A] := {A ∈ IRn×n : A ≤ A ≤ A}. By IRn×n we denote the set of all these so-called interval matrices. We also write [A] instead of [A,A]. The set of interval vectors with n components is constructed in the same way and denoted by IR. For an introduction to interval computations we refer to [2]. Let [q] ∈ IR and [M ] ∈ IRn×n be given. Then, we are interested in the set