178
Views
6
CrossRef citations to date
0
Altmetric
Original Article

A new exact algorithm for concave knapsack problems with integer variables

Pages 126-134 | Received 24 Jul 2016, Accepted 23 Nov 2017, Published online: 25 Jan 2018

References

  • R. Bellman and S.E. Dreyfus, Applied Dynamic Programming, Princeton University Press, Princeton, NJ, 1962.
  • H.P. Benson and S.S. Erengue, An algorithm for concave integer minimization over a polyhedron, Naval Res. Logist. 37 (1990), pp. 515–525. doi: 10.1002/1520-6750(199008)37:4<515::AID-NAV3220370406>3.0.CO;2-X
  • H.P. Benson, S.S. Erengue, and R. Horst, A note on adapting methods for continuous global optimization to the discrete case, Ann. Oper. Res. 25 (1990), pp. 243–252. doi: 10.1007/BF02283698
  • K.M. Bretthauer, A.V. Cabot, and M.A. Venkataramanan, An algorithm and new penalties for concave integer minimization over a polyhedron, Naval Res. Logist. 41 (1994), pp. 435–454. doi: 10.1002/1520-6750(199404)41:3<435::AID-NAV3220410309>3.0.CO;2-6
  • K.M. Bretthauer and B. Shetty, The nonlinear resource allocation problem, Oper. Res. 43 (1995), pp. 670–683. doi: 10.1287/opre.43.4.670
  • K.M. Bretthauer and B. Shetty, The nonlinear Knapsack problem – algorithms and applications, Eur. J. Oper. Res. 138 (2002), pp. 459–472. doi: 10.1016/S0377-2217(01)00179-5
  • K.M. Bretthauer and B. Shetty, A pegging algorithm for the nonlinear resource allocation problem, Comput. Oper. Res. 29 (2002), pp. 505–527. doi: 10.1016/S0305-0548(00)00089-7
  • A.V. Cabot and S.S. Erengue, A branch and bound algorithm for solving a class of nonlinear integer programming problems, Naval Res. Logist. 33 (1986), pp. 559–567. doi: 10.1002/nav.3800330403
  • D.S. Hochbaum, A nonlinear knapsack problem, Oper. Res. Lett. 17 (1995), pp. 103–110. doi: 10.1016/0167-6377(95)00009-9
  • R. Horst and N.V. Thoai, An integer concave minimization approach for the minimum concave cost capacitated flow problem on networks, OR Spektrum 20 (1998), pp. 47–53. doi: 10.1007/BF01545530
  • R. Horst and H. Tuy, Global Optimization: Deterministic Approaches, Springer-Verlag, Heidelberg, 1993.
  • R. Horst, P.M. Pardalos, and N.V. Thoai, Introduction to Global Optimization, 2nd ed., Nonconvex Optimization and Its Application, Vol. 48, Kluwer, Dordrecht, Netherlands, 2000.
  • D. Li, X.L. Sun, and F.L. Wang, Convergent Lagrangian and contour cut method for nonlinear integer programming with a quadratic objective function, SIAM J. Optim. 17 (2006), pp. 372–400. doi: 10.1137/040606193
  • R.E. Marsten and T.L. Morin, A hybrid approach to discrete mathematical programming, Math. Program. 14 (1978), pp. 21–40. doi: 10.1007/BF01588949
  • K. Mathur, H.M. Salkin, and S. Morito, A branch and search algorithm for a class of nonlinear knapsack problems, Oper. Res. Lett. 2 (1983), pp. 155–160. doi: 10.1016/0167-6377(83)90047-0
  • T.L. Morin and R.E. Marsten, Branch and bound strategies for dynamic programming, Oper. Res. 24 (1976), pp. 611–627. doi: 10.1287/opre.24.4.611
  • X.L. Sun, F.L. Wang, and D. Li, Exact algorithm for concave knapsack problems: Linear underestimation and partition method, J. Global Optim. 33 (2005), pp. 15–30. doi: 10.1007/s10898-005-1678-6

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.