# 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} }

## 17 Citations

On Fully Semimonotone Matrices

- MathematicsIGTR
- 2013

The main result of the paper shows that Stone's conjecture is true in the special case where the complementary cones have no partial incidence and an interesting characterization of Q0 for matrices with a special structure is presented.

Ju l 2 01 9 On Semimonotone Star Matrices and Linear Complementarity Problem

- Mathematics
- 2019

In this article, we introduce the class of semimonotone star (E 0) matrices. We establish the importance of E 0-matrix in the context of complementarity theory. We illustrate that the principal pivot…

Properties of some matrix classes based on principal pivot transform

- MathematicsAnn. Oper. Res.
- 2016

It is shown that a subclass of almost fully copositive matrices intorduced in (Linear Algebra Appl 400:243–252 2005) with $$Q_{0}$$Q0-property is captured by sufficient matrices introduced by Cottle et al.

A NOTE ON MURTHY'S CONJECTURE

- Mathematics
- 2007

In this paper, we consider a conjecture made by Murthy to the effect that a CQ f"l Qo matrix is positive semidefinite (PSD) and show that the conjecture is true for n x n matrices of rank 1 or 3 x 3…

On semimonotone star matrices and linear complementarity problem

- MathematicsOperators and Matrices
- 2021

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…

Relations between Semidefinite, Copositive, Semi-infinite and Integer Programming

- Computer Science
- 2010

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

- MathematicsJ. Glob. Optim.
- 2012

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

- MathematicsICMC
- 2021

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…

Total dual integrality and integral solutions of the linear complementarity problem

- MathematicsLinear Algebra and its Applications
- 2018

## References

SHOWING 1-10 OF 17 REFERENCES

Fully copositive matrices

- MathematicsMath. Program.
- 1998

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

- MathematicsSIAM J. Matrix Anal. Appl.
- 1995

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

- MathematicsSIAM J. Matrix Anal. Appl.
- 2000

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

- MathematicsMath. Program.
- 1989

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).

On Some Classes of Linear Complementarity Problems with Matrices of Order n and Rank (n - 1)

- MathematicsMath. Oper. Res.
- 1990

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

- Mathematics
- 1981

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…

The Linear Complementarity Problem

- Mathematics
- 1971

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…