45
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

GPM ANALYSIS IN COMBINING INTERIOR POINTS AND THE SIMPLEX METHOD

&
Pages 25-38 | Received 01 Aug 2001, Accepted 01 Feb 2002, Published online: 15 Feb 2010

  • Arbel , A. 1993 . Exploring Interior-Point Linear Programming Cambridge, Massachusetts : The MIT Press .
  • Bazaraa , M. S. and Shetty , C. M. 1979 . Nonlinear Programming Theory and Algorithms New York : John Wiley and Sons .
  • Bixby , R. E. , Gregory , J. W. , Lustig , I. J. , Marsten , R. E. and Shanno , D. F. 1992 . Very large-scale linear programming: a case study in combining interior point and simplex methods . Operations Research , 40 : 885 – 897 .
  • Dikin , I. I. 1967 . Iterative solution of problems of linear and quadratic programming . Soviet Mathematics Doklady , 8 : 674 – 675 .
  • Dikin , I. I. 1974 . O skhodimosti odnogo iteratsionnogo protsessa(in Russian) . Upravlyaemye Sistemy , 12 : 54 – 60 .
  • Fang , S. C. and Puthenpura , S. 1993 . Linear Optimization and Extensions Englewood Cliffs, New Jersey : Prentice-Hall .
  • Gondzio , J. 1993 . Implementing Cholesky factorization for interior point methods of linear programming . Optimization , 27 : 121 – 140 .
  • Huard , P. and Auslender , A. 1979 . Point-to-Set Maps and Mathematical Programming Amsterdam, New York : North-Holland Pub. Co. .
  • Karmarkar , N. K. 1984 . A new polynomial time algorithm for linear programming . Combinatorica , 4 : 373 – 395 .
  • Luh , H. and Tsaih , R. 2002 . An efficient search direction for linear programming problems . Computers and Operations Research , 29 : 195 – 203 .
  • Megiddo , N. 1991 . On finding primal and dual optimal bases . ORSA J. on Comput. , 3 : 63 – 65 .
  • Rosen , J. B. 1960 . The gradient projection method for nonlinear programming. Part 1: linear constraints . SIAM Jounal on Application Mathematics , 9 : 514 – 553 .
  • Terlaky , T. 1996 . Interior Point Methods of Mathematical Programming Dordrecht, , Netherlands : Kluwer Academic publishers .
  • Trefethen , L. N. and Bau , D. 1997 . Numerical linear algebra . The Society for Industrial and Applied Mathematics , 7 : 276 – 319 .
  • Vanderbei , R. J. , Meketon , M. S. and Freedman , B. A. 1986 . A modiffication of Karmarkar's linear programming algorithm . Algorithmica , 1 : 395 – 407 .
  • Vanderbei , R. J. 1989 . Affine-scaling for linear programs with free variables . Mathematical Programming , 43 : 31 – 44 .
  • Vavasis , S. A. and Ye , Y. 1996 . Identifying an optimal basis in linear programming . Annals of Operations Research , 62 : 565 – 572 .
  • Winston , W. L. 1994 . Operations Research Applitions and Algorithms New York : Duxbury Press .
  • Ye , Y. 1997 . Interior Point Algorithms Theory and Analysis New York : John Wiley and Sons .

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.