On the classes of fully copositive and fully semimonotone matrices

@article{Mohan2001OnTC,
  title={On the classes of fully copositive and fully semimonotone matrices},
  author={S. R. Mohan and S. K. Neogy and A. K. Das},
  journal={Linear Algebra and its Applications},
  year={2001},
  volume={323},
  pages={87-97}
}
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17 Citations
Background Citations
4
Results Citations
1

17 Citations

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On semimonotone star matrices and linear complementarity problem
In this article, we introduce the class of semimonotone star ($E_0^s$) matrices. We establish the importance of the class of $E_0^s$-matrices in the context of complementarity theory. We show that…
On hidden Z-matrices and the linear complementarity problem
Relations between Semidefinite, Copositive, Semi-infinite and Integer Programming
TLDR
This thesis will investigate the relationship to answer the question whether one can solve semidefinite program by formulating it as an equivalent eigenvalue optimization with the aid of semi-infinite programming.
Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization
TLDR
A systematic construction principle for non-attainability phenomena, which apparently has not been noted before in an explicit way is presented, and for the first time, a somehow systematic clustering of the vast and scattered literature is attempted.
On Column Competent Matrices and Linear Complementarity Problem
Abstract We revisit the class of column competent matrices and study some matrix theoretic properties of this class. The local w-uniqueness of the solutions to the linear complementarity problem can…
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References

SHOWING 1-10 OF 17 REFERENCES
Fully copositive matrices
The class of fully copositive (C0f) matrices introduced in [G.S.R. Murthy, T. Parthasarathy, SIAM Journal on Matrix Analysis and Applications 16 (4) (1995) 1268–1286] is a subclass of fully…
Some Properties of Fully Semimonotone, Q0-Matrices
TLDR
It is shown that the conjecture that the same must be true for fully semimonotone ($E^{f}_{0}$) matrices is true for matrices of order up to $4 \times 4$ and partially resolve it for higher order matrices.
On the Solution Sets of Linear Complementarity Problems
TLDR
It is shown that the solution sets arising from LCPs with $C_0^f\cap Q_0$-matrices and their transposes are convex, which means that C_ 0^f \cap Q-matrix are sufficient matrices, another well known class in the theory of linear complementarity problem.
On strongly degenerate complementary cones and solution rays
TLDR
It is shown that ifA is a matrix in the class of matricesE(d), for ad ∈Rn,d > 0, then the boundary of the set ofq ∈ Rn for which the linear complementarity problem (q, A) has a solution is equal to the union of all strongly degenerate cones of (I, -A).
Sufficient matrices and the linear complementarity problem
On Some Classes of Linear Complementarity Problems with Matrices of Order n and Rank (n - 1)
TLDR
Two subclasses of the class of n × n matrices M of rank ( n − 1) for which the set of q ∈ R n such that the LCP ( q, M ) has a solution is convex are identified.
Geometric aspects of the linear complementarity problem
Abstract : A large part of the study of the Linear Complementarity Problem (LCP) has been concerned with matrix classes. A classic result of Samelson, Thrall, and Wesler is that the real square…
On classes of copositive matrices
Two characterizations of sufficient matrices
The Linear Complementarity Problem
This study centers on the task of efficiently finding a solution of the linear complementarity problem: Ix - My = q, x \ge 0, y \ge 0, x \perp y. The main results are: (1) It is shown that Lemke's…
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