NP-hardness of linear multiplicative programming and related problems

Journal of Global Optimization

Volumn 9, Issue 2, 1996, Pages 113-119

  Matsui, T ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Linear fractional programming; Linear multiplicative programming; Minimization of products; Multi ratio programming; NP hard

Indexed keywords

EID: 0000108196     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00121658     Document Type: Article

References (15)

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.
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.
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.
6. Konno, H. and Kuno, T. (1992), Linear multiplicative programming, Mathematical Programming 56, 51-64.
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.
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.
11. Pardalos, P.M. (1990), Polynomial time algorithms for some classes of constrained nonconvex quadratic problems, Optimization 21, 843-853.
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.
13. Swarup, K. (1966), Indefinite quadratic programming, Cahiers du Centre d'Etudes de Recherche Operationnelle 8, 217-222.
14. Thoai, N.V. (1991), A global optimization approach for solving the convex multiplicative programming problem, Journal of Global Optimization 1, 341-357.
15. Tuy, H. and Tam, B.T. (1992), An efficient solution method for rank two quasiconcave minimization problems, Optimization 24, 43-56.