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On solving a non-convex quadratic programming problem involving resistance distances in graphs

  • S.I.: Game theory and optimization
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Abstract

Quadratic programming problems involving distance matrix (D) that arises in trees are considered in the literature by Dankelmann (Discrete Math 312:12–20, 2012), Bapat and Neogy (Ann Oper Res 243:365–373, 2016). In this paper, we consider the question of solving the quadratic programming problem of finding maximum of \(x^{T}Rx\) subject to x being a nonnegative vector with sum 1 and show that for the class of simple graphs with resistance distance matrix (R) which are not necessarily a tree, this problem can be reformulated as a strictly convex quadratic programming problem. An application to symmetric bimatrix game is also presented.

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Acknowledgements

The authors would like to thank the anonymous referees for their constructive suggestions which considerably improve the overall presentation of the paper. The authors would like to thank Professor R. B. Bapat, Indian Statistical Institute, Delhi Centre for his valuable comments and suggestions. The first author wants to thank the Science and Engineering Research Board, Department of Science & Technology, Government of India, for financial support for this research.

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Authors and Affiliations

  1. Indian Statistical Institute, 7, S. J. S. Sansanwal Marg, New Delhi, 110016, India

    Dipti Dubey & S. K. Neogy

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  1. Dipti Dubey
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  2. S. K. Neogy
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Correspondence to S. K. Neogy.

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Dubey, D., Neogy, S.K. On solving a non-convex quadratic programming problem involving resistance distances in graphs. Ann Oper Res 287, 643–651 (2020). https://doi.org/10.1007/s10479-018-3018-5

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  • DOI: https://doi.org/10.1007/s10479-018-3018-5

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