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

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Listed:
  • Dipti Dubey

    (Indian Statistical Institute)

  • S. K. Neogy

    (Indian Statistical Institute)

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 $$x^{T}Rx$$xTRx 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.

Suggested Citation

  • Dipti Dubey & S. K. Neogy, 2020. "On solving a non-convex quadratic programming problem involving resistance distances in graphs," Annals of Operations Research, Springer, vol. 287(2), pages 643-651, April.
    • Handle: RePEc:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-018-3018-5
    DOI: 10.1007/s10479-018-3018-5
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    References listed on IDEAS

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    1. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    2. Éva Tardos, 1986. "A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs," Operations Research, INFORMS, vol. 34(2), pages 250-256, April.
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