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Erschienen in:
2018 | OriginalPaper | Buchkapitel
On Generalized Positive Subdefinite Matrices and Interior Point Algorithm
verfasst von : A. K. Das, R. Jana, Deepmala
Erschienen in: Operations Research and Optimization
Verlag: Springer Singapore
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Abstract
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 generalized positive subdefinite matrices (GPSBD) which is a generalization of the class of positive subdefinite (PSBD) 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 GPSBD class. We provide the complexity analysis of the proposed algorithm. A numerical example is illustrated to show the performance of the proposed algorithm.