On Generalized Positive Subdefinite Matrices and Interior Point Algorithm

  • A. K. Das
  • R. Jana
  • Deepmala
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 225)


In this paper, we propose an iterative and descent type interior point method to compute solution of linear complementarity problem LCP(qA) 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(qA), 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(qA) 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.


Interior point algorithm Generalized positive subdefinite matrices (GPSBD) Positive subdefinite matrices (PSBD) Linear complementarity problem 



The second author R. Jana is thankful to the Department of Science and Technology, Govt. of India, INSPIRE Fellowship Scheme for financial support. The research work of the third author Deepmala is supported by the Science and Engineering Research Board (SERB), Government of India under SERB N-PDF scheme, File Number: PDF/2015/000799.


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Indian Statistical InstituteKolkataIndia
  2. 2.Jadavpur UniversityKolkataIndia
  3. 3.Mathematics DisciplinePDPM Indian Institute of Information Technology, Design and ManufacturingJabalpurIndia

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