Abstract
In this note, we show that LipschitzianQ-matrices areP-matrices by obtaining a necessary condition on LipschitzianQ 0-matrices. The sufficiency of this condition has also been established by the first two authors along with another coauthor (Murthy, Parthasarathy and Sriparna, 1995).
Similar content being viewed by others
References
R.W. Cottle, J.S. Pang and R.E. Stone,The Linear Complementarity Problem (Academic Press, New York, 1992).
M.S. Gowda, On the continuity of the solution map in linear complementarity problems,SIAM Journal of Optimization 2 (1992) 619–634.
M.S. Gowda, Applications of degree theory to linear complementarity problems,Mathematics of Operations Research 18 (4) (1993) 868–878.
O.L. Mangasarian and T.H. Shiau, Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems,SIAM Journal on Control and Optimization 25 (1987) 583–595.
G.S.R. Murthy, T. Parthasarathy and B. Sriparna, Constructive characterization of LipschitzianQ 0-matrices, Technical Report No. 23 (1995), Indian Statistical Institute, Madras, India to appear inLinear Algebra and Its Applications.
K.G. Murty,Linear Complementarity, Linear and Nonlinear Programming (Heldermann Verlag, Berlin, 1988).
C. Olech, T. Parthasarathy, and G. Ravindran, AlmostN-matrices and its applications to linear complementarity problem and global univalence,Linear Algebra and its Applications 145 (1991) 107–125.
T.D. Parsons, Applications of principal pivoting, in H.W. Kuhn, ed.,Proceedings of the Princeton Symposium on Mathematical Programming (Princeton Univ. Press, Princeton, NJ, 1970) 561–581.
Author information
Authors and Affiliations
Additional information
This work was done while I visited ISI, Delhi Center during March–April, 1994. I want to express my sincere thanks for their kind hospitality.
Rights and permissions
About this article
Cite this article
Murthy, G.S.R., Parthasarathy, T. & Sabatini, M. LipschitzianQ-matrices areP-matrices. Mathematical Programming 74, 55–58 (1996). https://doi.org/10.1007/BF02592146
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02592146