On the classes of fully copositive and fully semimonotone matrices

  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},
On Fully Semimonotone Matrices
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
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
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.
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
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
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
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


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
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
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
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)
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
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