Criteria for sufficient matrices

Abstract Column sufficient, row sufficient, and sufficient matrices have recently arisen in connection with the linear complementarity problem. We review and supplement the basic theory of these matrix classes, propose new criteria for identifying them, and compare these criteria with the existing ones. Our main mathematical tool is principal pivoting.

[1]  Richard W. Cottle.  The principal pivoting method revisited , 1990, Math. Program..

[2]  M. Fiedler.  On inverting partitioned matrices , 1963 .

[3]  G. Dantzig,et al.  COMPLEMENTARY PIVOT THEORY OF MATHEMATICAL PROGRAMMING , 1968 .

[4]  H. Kuhn.  Proceedings of the Princeton Symposium on Mathematical Programming , 1971 .

[5]  Richard W. Cottle,et al.  Least-Index Resolution of Degeneracy in Linear Complementarity Problems with Sufficient Matrices , 1979, SIAM J. Matrix Anal. Appl..

[6]  T. Parsons.  A combinatorial approach to convex quadratic programming , 1970 .

[7]  A. W. Tucker,et al.  Duality Theory of Linear Programs: A Constructive Approach with Applications , 1969 .

[8]  M. Fiedler,et al.  On matrices with non-positive off-diagonal elements and positive principal minors , 1962 .

[9]  Tamás Terlaky,et al.  The linear complimentarity problem, sufficient matrices, and the criss-cross method , 1993 .

[10]  R. Cottle,et al.  Sufficient matrices and the linear complementarity problem , 1989 .

[11]  M. Fiedler,et al.  Some generalizations of positive definiteness and monotonicity , 1966 .

[12]  G. Styan,et al.  Equalities and Inequalities for Ranks of Matrices , 1974 .

[13]  Richard W. Cottle,et al.  On the uniqueness of solutions to linear complementarity problems , 1983, Math. Program..

[14]  L. Mirsky,et al.  The Theory of Matrices , 1961, The Mathematical Gazette.

[15]  H. Väliaho.  A procedure for the one-parametric linear complementarity problem , 1994 .

[16]  Richard W. Cottle,et al.  Two characterizations of sufficient matrices , 1992 .

[17]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .