On generalized positive subdefinite matrices and interior point algorithm
Springer Proceedings in Mathematics and Statistics
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.
Das, A. K.; Jana, R.; and Deepmala, "On generalized positive subdefinite matrices and interior point algorithm" (2018). Conference Articles. 164.