Solution of parametric vertical block linear complementarity problems

The parametric vertical block linear complementarity problem is introduced where the associated vertical block matrix and the column vector are parametric. Assuming the matrix to be a vertical block P-matrix, an algorithm is developed for solving vertical block linear complementarity problems. A necessary and sufficient condition is also derived to ensure the same solution basis for any parametric input of the vertical block P-matrix. Based on these, an algorithm is proposed and the solution of the parametric vertical block linear complementarity problem is obtained. A numerical example is presented to illustrate the use of the method.