On hidden Z-matrix and interior point algorithm
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We propose an interior point method to compute solution of linear complementarity problem LCP (q, A) given that A is a real square hidden Z-matrix (generalization of Z-matrix) and q is a real vector. The class of hidden Z-matrix is important in the context of mathematical programming and game theory. We study the solution aspects of linear complementarity problem with \(A \in\) hidden Z-matrix. We observe that our proposed algorithm can process LCP (q, A) in polynomial time under some assumptions. Two numerical examples are illustrated to support our result.
KeywordsZ-matrix Hidden Z-matrix Simplex method Interior point algorithm Linear complementarity problem
Mathematics Subject Classification90C33 90C51
The author A. Dutta is thankful to the Department of Science and Technology, Govt. of India, INSPIRE Fellowship Scheme for financial support. The authors are grateful to the anonymous reviewers and Professor Ashis Kumar Chakraborty, the guest editor for their valuable comments and suggestions to improve the quality of the paper.
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