On semimonotone star matrices and linear complementarity problem
Operators and Matrices
In this article, we introduce the class of semimonotone star ( E0s ) matrices. We establish the importance of the class of E0s-matrices in the context of complementarity theory. We show that the principal pivot transform of an E0s-matrix is not necessarily Es0 in general. How-ever, we prove that E˜0s-matrices, a subclass of the Es0-matrices with some additional conditions, is fully semimonotone matrix by showing this class is in P0 . We prove that LCP (q, A) can be processable by Lemke’s algorithm if A ∈ E˜ 0s ∩ P0. We find some conditions for which the solution set of LCP(q, A) is bounded and stable under the E˜ 0s-property. We propose an algorithm based on an interior point method to solve LCP(q, A) given A ∈ E˜ 0s..
Jana, R.; Das, A. K.; and Sinha, S., "On semimonotone star matrices and linear complementarity problem" (2021). Journal Articles. 2036.
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