Journal ArticleDOI
On generalizations of positive subdefinite matrices and the linear complementarity problem
Dipti Dubey,S. K. Neogy +1 more
TLDR
The notion of generalized positive subdefinite matrices of level k is introduced by generalizing the definition of generalized Positive Subdefinite Matrices introduced by Crouzeix and Komlósi in [Applied optimization].Abstract:
In this paper, we introduce the notion of generalized positive subdefinite matrices of level k by generalizing the definition of generalized positive subdefinite matrices introduced by Crouzeix and Komlosi in [Applied optimization. Vol. 59, Dordrecht: Kluwer Academic Publications; 2001. p. 45–63]. The main motivation behind this generalization is to identify new subclasses of row sufficient matrices [Cottle, Pang and Venkateswaran, Linear Algebra Appl. 1989;114/115:231–249] which are not a subclass of copositive matrices. We establish new sufficient conditions for a matrix to be a non-copositive matrix and a non-copositive row sufficient matrix using the notion of generalized positive subdefinite matrices of level k. We present a new termination result for Lemke’s algorithm which supplements Jones’ result [Math Program. 1986;35:239–242].read more
References
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Journal ArticleDOI
Two characterizations of sufficient matrices
Richard W. Cottle,Sy-Ming Guu +1 more
TL;DR: In this article, two characterizations for the class of sufficient matrices defined by Cottle, Pang, and Venkateswaran are given for linear programming terms.
Journal ArticleDOI
On the transposition anti-involution in real Clifford algebras III: the automorphism group of the transposition scalar product on spinor spaces
TL;DR: Ablamowicz and Fauser as discussed by the authors proposed a transposition map for real Clifford algebras Cl p,q for non-degenerate quadratic forms and showed that the map gives rise to complex Hermitian or quaternionic Hermitians in spinor representation.
Journal ArticleDOI
Modified modulus-based matrix splitting iteration methods for linear complementarity problems
TL;DR: For solving the large sparse linear complementarity problems, modified modulus-based matrix splitting iteration methods are established and the convergence analysis when the system matrices are H+-matrices is presented.
Journal ArticleDOI
On weak generalized positive subdefinite matrices and the linear complementarity problem
S. K. Neogy,A. K. Das +1 more
TL;DR: In this paper, a weaker version of the class of generalized positive subdefinite matrices introduced by Crouzeix and Komlosi is presented, which is new in the literature, and obtain some properties of weak generalized PSBD matrices.
Journal ArticleDOI
More with the Lemke complementarity algorithm
TL;DR: In the case that the matrix of a linear complementarity problem consists of the sum of a positive semi-definite matrix and a co-positive matrix a general condition is deduced implying that the Lemke algorithm will terminate with a complementarity solution.
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On weak generalized positive subdefinite matrices and the linear complementarity problem
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