119
Views
7
CrossRef citations to date
0
Altmetric
Section B

A hybrid direction algorithm for solving linear programs

&
Pages 201-216 | Received 12 May 2013, Accepted 28 Jan 2014, Published online: 27 Mar 2014

References

  • M. Bentobache, On mathematical methods of linear and quadratic programming, PhD thesis, University of Bejaia, Bejaia, 2013.
  • M. Bentobache and M.O. Bibi, Adaptive method with hybrid direction: Theory and numerical experiments, in Proceedings of Optimization’2011, University of Lisbon, Portugal, 24–27 July 2011, pp. 112.
  • M. Bentobache and M.O. Bibi, A two-phase support method for solving linear programs: Numerical experiments, Mathematical Problems in Engineering, 2012, Article ID 482193, 28 pages, 10.1155/2012/482193.
  • M.O. Bibi, Support method for solving a linear-quadratic problem with polyhedral constraints on control, Optimization 37(2) (1996), pp. 139–147. doi: 10.1080/02331939608844205
  • M.O. Bibi and M. Bentobache, The Adaptive method with hybrid direction for solving linear programming problems with bounded variables, in Proceedings of COSI’2011, University of Guelma, Algeria, 24–27 April 2011, pp. 80–91.
  • M.O. Bibi and M. Bentobache, A hybrid direction algorithm for solving linear programs, in Proceedings of DIMACOS’11, University of Mohammedia, Morocco, 5–8 May 2011, pp. 28–30.
  • B. Brahmi and M.O. Bibi, Dual support method for solving convex quadratic programs, Optimization 59(6) (2010), pp. 851–872. doi: 10.1080/02331930902878341
  • G.B. Dantzig, Maximization of a linear function of variables subject to linear inequalities, in Activity Analysis of Production and Allocation, R.C. Koopmans, ed., Wiley, New York, 1951, pp. 339–347.
  • G.B. Dantzig, Linear Programming and Extensions, Princeton University Press, Princeton, NJ, 1963.
  • M.C. Ferris, O.L. Mangasarian, and S.J. Wright, Linear Programming with MATLAB, MPS-SIAM Series on Optimization, Philadelphia, 2007.
  • R. Gabasov and F.M. Kirillova, Methods of Linear Programming, Vols. 1, 2 and 3, Edition of the Minsk University, Minsk, 1977, 1978, 1980 (in Russian).
  • R. Gabasov, F.M. Kirillova, and O.I. Kostyukova, Solution of linear quadratic extremal problems, Soviet Math Doklady 31 (1985), pp. 99–103.
  • R. Gabasov, F.M. Kirillova, and O.I. Kostyukova, A method of solving general linear programming problems, Doklady AN BSSR 23(3) (1979), pp. 197–200 (in Russian).
  • R. Gabasov, F.M. Kirillova, and S.V. Prischepova, Optimal Feedback Control, Springer-Verlag, London, 1995.
  • M. Gay, Electronic mail distribution of linear programming test problems, Math. Program. Soc. COAL Bull. 13 (1985), pp. 10–12. Available at http://www.netlib.org/lp/data.
  • E. Kostina, The long step rule in the bounded-variable dual simplex method: Numerical experiments, Math. Methods Oper. Res. 55 (2002), pp. 413–429. doi: 10.1007/s001860200188
  • E.A. Kostina and O.I. Kostyukova, An algorithm for solving quadratic programming problems with linear equality and inequality constraints, Comput. Math. Math. Phys. 41(7) (2001), pp. 960–973.
  • P-Q. Pan, A basis-deficiency-allowing variation of the simplex method, Comput. Math. Appl. 36(3) (1998), pp. 33–53. doi: 10.1016/S0898-1221(98)00127-8
  • K. Paparrizos, N. Samaras, and G. Stephanides, An efficient simplex type algorithm for sparse and dense linear programs, Eur. J. Oper. Res. 148 (2003), pp. 323–334. doi: 10.1016/S0377-2217(02)00400-9
  • S. Radjef and M.O. Bibi, An effective generalization of the direct support method, Math. Probl. Eng. Vol. 2011, Article ID 374390, 18 pages, 10.1155/2011/374390.

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.