A parametric linear complementarity problem involving derivatives

The problem considered in this paper is given by the conditions:w = q + tp + Mz, w ≥ 0, ż ≥ 0, w^Tż = 0, where a dot denotes the derivative with respect to the scalar parameter t ≥ 0. In this problem, q, p are n-vectors with q ≥ 0 and M is a n by n P-matrix. This problem arises in a certain basic problem in the field of structural mechanics. The main result in this paper is the existence and uniqueness theorem of a solution to this problem. The existence proof is constructive providing a computational method of obtaining the solution asymptotically.