Solution of parametric vertical block linear complementarity problems

Abstract

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.

Keywords:

• Parametric linear complementarity problem
• Vertical block matrix
• Vertical block linear complementarity problem
• P-matrix
• Vertical block P-matrix

Acknowledgements

The authors are grateful to the anonymous referees for their helpful comments and suggestions, which improved the quality and presentation of the paper.

Additional information

Notes on contributors

B. Chakraborty

Email: [email protected]