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NP-hardness of linear multiplicative programming and related problems

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Abstract

The linear multiplicative programming problem minimizes a product of two (positive) variables subject to linear inequality constraints. In this paper, we show NP-hardness of linear multiplicative programming problems and related problems.

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References

  1. Aneja, Y.P., Aggarwal, V. and Nair, K.P.K. (1984), ‘On a class of quadratic programs’, European Journal of Operational Research 18, 62–70.

    Google Scholar 

  2. Garey, M.R. and Johnson, D.S. (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman.

  3. Karp, R.M. (1972), Reducibility among combinatorial problems. in Complexity of Computer Computations (R.E. Miller and J.W. Thatcher eds.), Plenum Press.

  4. Konno, H. and Kuno, T. (1990), Generalized linear multiplicative and fractional programming, Annals of Operations Research 25, 147–162.

    Google Scholar 

  5. Konno, H., Yajima, Y. and Matsui, T. (1991), Parametric simplex algorithms for solving a special class of nonconvex minimization problems, Journal of Global Optimization 1, 65–82.

    Google Scholar 

  6. Konno, H. and Kuno, T. (1992), Linear multiplicative programming, Mathematical Programming 56, 51–64.

    Google Scholar 

  7. Konno, H., Kuno, T. and Yajima, Y. (1992), Parametric simplex algorithms for a class of NP complete problems whose average number of steps are polynomial, Computational Optimization and Applications 1, 227–239.

    Google Scholar 

  8. Konno, H. and Kuno, T. (1995), Multiplicative programming problems, in Handbook of Global Optimization (R. Horst and P.M. Pardalos eds.), Kluwer Academic Publishers.

  9. Konno, H., Thach, P.T. and Tuy, H. Global Optimization: Low Rank Nonconvex Structures, Kluwer Academic Publishers (to appear).

  10. Kuno, T. and Konno, H. (1991), A parametric successive underestimation method for convex multiplicative programming problems, Journal of Global Optimization 1, 267–285.

    Google Scholar 

  11. Pardalos, P.M. (1990), Polynomial time algorithms for some classes of constrained nonconvex quadratic problems, Optimization 21, 843–853.

    Google Scholar 

  12. Pardalos, P.M. and Vavasis, S.A. (1991), Quadratic programming with one negative eigen-value is NP-hard, Journal of Global Optimization 1, 15–22.

    Google Scholar 

  13. Swarup, K. (1966). Indefinite quadratic programming, Cahiers du Centre d'Etudes de Recherche Operationnelle 8, 217–222.

    Google Scholar 

  14. Thoai, N.V. (1991), A global optimization approach for solving the convex multiplicative programming problem, Journal of Global Optimization 1, 341–357.

    Google Scholar 

  15. Tuy, H. and Tam, B.T. (1992), An efficient solution method for rank two quasiconcave minimization problems, Optimization 24, 43–56.

    Google Scholar 

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Matsui, T. NP-hardness of linear multiplicative programming and related problems. J Glob Optim 9, 113–119 (1996). https://doi.org/10.1007/BF00121658

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  • DOI: https://doi.org/10.1007/BF00121658

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