On Semimonotone Star Matrices and Linear Complementarity Problem
Abstract
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 the principal pivot transform of $E_0^s$-matrix is not necessarily $E_0^s$ in general. However, we prove that $\tilde{E_0^s}$-matrices, a subclass of the $E_0^s$-matrices with some additional conditions, is in $E_0^f$ by showing this class is in $P_0.$ We prove that LCP$(q, A)$ can be processable by Lemke's algorithm if $A\in \tilde{E_0^s}\cap P_0.$ We find some conditions for which the solution set of LCP$(q, A)$ is bounded and stable under the $\tilde{E^s_0}$-property. We propose an algorithm based on an interior point method to solve LCP$(q, A)$ given $A \in \tilde{E^{s}_{0}}.$
- Publication:
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arXiv e-prints
- Pub Date:
- August 2018
- DOI:
- 10.48550/arXiv.1808.00281
- arXiv:
- arXiv:1808.00281
- Bibcode:
- 2018arXiv180800281J
- Keywords:
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- Mathematics - Optimization and Control