On the Convergence of an Iterative Method for Solving Linear Complementarity Problem with WGPSBD Matrix

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Research Article

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Thai Journal of Mathematics


In this paper we propose an iterative and descent type interior point method to compute solution of linear complementarity problem LCP(q, A) given that A is real square matrix and q is a real vector. The linear complementarity problem includes many of the optimization problems and applications. In this context we consider the class of weak generalized positive subdefinite matrices (WGPSBD) which is a generalization of the class of generalized positive subdefinite (GPSBD) matrices. Though Lemke’s algorithm is frequently used to solve small and medium size LCP(q, A), Lemke’s algorithm does not compute solution of all problems. It is known that Lemke’s algorithm is not a polynomial time bound algorithm. We show that the proposed algorithm converges to the solution of LCP(q, A) where A belongs to WGPSBD class. A numerical example is illustrated to show the performance of the proposed algorithm.

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