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Enumerative methods in nonconvex programming

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Constrained Global Optimization: Algorithms and Applications

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 268))

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References

  1. Al-Khayyal, F.A. An implicit enumeration algorithm for the general linear complementarity problem. Tech. Report, School of Indust. and Syst. Engin., The Georgia Inst. of Technology (1985).

    Google Scholar 

  2. Balinski, M.L. An algorithm for finding all vertices of polyhedral sets. J. Soc. Indust. Appl. Math. 9 (1961), 72–89.

    Article  Google Scholar 

  3. Bazara, M.S. and Sherali, H.D. A versatile scheme for ranking the extreme points of an assignment polytope. Naval Research Log. Quart. Vol. 28 (1981), No. 4.

    Google Scholar 

  4. Cabot, V.A. and Francis, R.L. Solving certain nonconvex quadratic minimization problems by ranking the extreme points. Operations Research, Vol. 18 (1970), 82–86.

    Google Scholar 

  5. Chvatal, V. Linear Programming. Freeman N.Y. (1983)

    Google Scholar 

  6. Burdet., C.A. Generating all faces of a polyhedron. SIAM J. Appl. Math. 26 (1974), 72–89.

    Article  Google Scholar 

  7. Dahl, G. and Storoy, S. Decomposed enumeration of extreme points in the linear programming problem. BIT 15 (1975), 151–157.

    Article  Google Scholar 

  8. Dyer, M.E. The complexity of vertex enumeration methods. Math. Oper. Res. 8 (1983), 381–402.

    Google Scholar 

  9. Dyer, M.E. and Proll, L.G. An algorithm for determining all extreme points of a convex polytope. Math. Progr. 12 (1977), 81–96.

    Article  Google Scholar 

  10. Florian, M. and Robillard, P. An implicit enumeration algorithm for the concave cost network flow problem. Manag. Science, Vol 18 (1971), 184–193.

    Google Scholar 

  11. Judice, J.J. and Mitra, G. An enumerative method for the solution set of linear complementarity problems. Working Paper, Math. Dept., Brunel Univer. (1985).

    Google Scholar 

  12. Linial, N. Hard enumeration problems in geometry and combinatorics. SIAM J. Alg. Discr. Meth. Vol. 7, No 2 (1986), 331–335.

    Google Scholar 

  13. Lozovanu, D.D. Properties of optimal solutions of a grid transport problem with concave cost function of the flow on the arcs. Engin. Cybernetics Vol. 20 (1982), 34–38.

    Google Scholar 

  14. Matheiss, T.H. and Rubin, D.S. A survey and comparison of methods for finding all vertices of convex polyhedral sets. Math. Oper. Reser. 5 (1980), 167–185.

    Google Scholar 

  15. McKeown, P.G. Extreme point ranking algorithms: A computational survey. In Computers and Math. Progr., W.W. White ed., National Bureau of Standards Special Publication 502 (1978), U.S. Government Printing Office, Washington DC, 216–222.

    Google Scholar 

  16. Manas, M. An algorithm for a nonconvex programming problem. Econom. Math. Obzor, Acad. Nacl. Ceskoslov. (1968), 202–212.

    Google Scholar 

  17. Manas, M. and Nedoma, J. Finding all vertices of a convex polyhedral set. Numer. Mathem. 9 (1974), 35–39.

    Google Scholar 

  18. Martos, B. Nonlinear Programming: theory and methods North-Holland Publishing Company, (1975).

    Google Scholar 

  19. Murty, K.G. Solving the fixed charge problem by ranking the extreme points. Operations Research, Vol 18 (1968), 268–279.

    Google Scholar 

  20. Murty, K.G. Linear Programming Wiley (1983).

    Google Scholar 

  21. Pardalos, P.M. An algorithm for a class of nonlinear fractional problems using ranking of the vertices. BIT 26 (1986), 392–395.

    Article  Google Scholar 

  22. Rossler, M. A method to calculate an optimal production plan with a concave objective function. Unternehmnsforschung, 20 (1973), 373–382.

    Google Scholar 

  23. Schmidt, B.K. and Mattheiss, T.H. Computational results on an algorithm for finding all vertices of a polytope. Math. Progr. Vol. 18 (1980), 308–329.

    Article  Google Scholar 

  24. Storoy, S. Ranking of vertices in the linear fractional programming problem. BIT 23 (1983), No. 3, 403–405.

    Article  Google Scholar 

  25. Taha, H.A. Concave minimum over a convex polyhedron. Naval Res. Logist. Quart. Vol. 20 (1973), 353–355.

    Google Scholar 

  26. Valiant, L.J. The complexity of enumeration and reliability problems. SIAM J. Comput., Vol 8 (1979), 410–421.

    Google Scholar 

  27. Zangwill, W.I. Minimum concave cost flows in certain networks. Manag. Science. Vol 14 (1968), 429–450.

    Google Scholar 

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Panos M. Pardalos J. Ben Rosen

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© 1987 Springer-Verlag

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(1987). Enumerative methods in nonconvex programming. In: Pardalos, P.M., Rosen, J.B. (eds) Constrained Global Optimization: Algorithms and Applications. Lecture Notes in Computer Science, vol 268. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000039

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  • DOI: https://doi.org/10.1007/BFb0000039

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18095-1

  • Online ISBN: 978-3-540-47755-6

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