More results on column sufficiency property in Euclidean Jordan algebras

A matrix M∈Rn×n is said to be a column sufficient matrix if the solution set of LCP(M,q) is convex for every q∈Rn. In a recent article, Qin et al. (Optim. Lett. 3:265–276, 2009) studied the concept of column sufficiency property in Euclidean Jordan algebras. In this paper, we make a further study of this concept and prove numerous results relating column sufficiency with the Z and Lypaunov-like properties. We also study this property for some special linear transformations.

[1]  Strict Semimonotonicity Property of Linear Transformations on Euclidean Jordan Algebras , 2010 .

[2]  M. Seetharama Gowda,et al.  Complementarity forms of theorems of Lyapunov and Stein, and related results , 2000 .

[3]  T. Damm.  Positive groups on Hn are completely positive , 2004 .

[4]  M. Seetharama Gowda,et al.  Some P-Properties for Nonlinear Transformations on Euclidean Jordan Algebras , 2005, Math. Oper. Res..

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

[6]  J. Faraut,et al.  Analysis on Symmetric Cones , 1995 .

[7]  S. Karamardian.  An existence theorem for the complementarity problem , 1976 .

[8]  M. Seetharama Gowda,et al.  Z-transformations on proper and symmetric cones , 2008, Math. Program..

[9]  R. Sznajder,et al.  Some P-properties for linear transformations on Euclidean Jordan algebras , 2004 .

[11]  Lingchen Kong,et al.  Sufficiency of linear transformations on Euclidean Jordan algebras , 2009, Optim. Lett..

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

[13]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[14]  F. Facchinei,et al.  Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .

[15]  M. Seetharama Gowda,et al.  Automorphism Invariance of P- and GUS-Properties of Linear Transformations on Euclidean Jordan Algebras , 2006, Math. Oper. Res..

[16]  Richard W. Cottle,et al.  On a subclass of P0 , 1995 .