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International Conference on Frontiers in Optimization: Theory and Applications

FOTA 2016: Operations Research and Optimization pp 3–16Cite as

On Generalized Positive Subdefinite Matrices and Interior Point Algorithm

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 225))

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.

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Acknowledgements

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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Authors and Affiliations

  1. Indian Statistical Institute, 203 B. T. Road, Kolkata, 700108, India

    A. K. Das &  Deepmala

  2. Jadavpur University, Kolkata, 700032, India

    R. Jana

  3. Mathematics Discipline, PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, 482005, India

    Deepmala

Authors
  1. A. K. Das
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  2. R. Jana
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  3. Deepmala
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Corresponding author

Correspondence to Deepmala .

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Editors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, West Bengal, India

    Samarjit Kar

  2. Department of Computer Science and Engineering, Jadavpur University, Kolkata, West Bengal, India

    Ujjwal Maulik

  3. School of Economics and Management, Beijing University of Chemical Technology, Beijing, China

    Xiang Li

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Das, A.K., Jana, R., Deepmala (2018). On Generalized Positive Subdefinite Matrices and Interior Point Algorithm. In: Kar, S., Maulik, U., Li, X. (eds) Operations Research and Optimization. FOTA 2016. Springer Proceedings in Mathematics & Statistics, vol 225. Springer, Singapore. https://doi.org/10.1007/978-981-10-7814-9_1

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