Interior-point methods for linear programming: a review

References

• DEN HERTOG , D . 1994 . Interior point Approach to Linear, Quadratic and Convex Programming, Algorithms and Complexity , Dordrecht : Kluwer .
   Google Scholar
• DIKIN , L. L . 1967 . Sov. Math., Doklady , 8 : 675 – 679 .
   Google Scholar
• DIKIN , L. L . 1974 . Upravlyaemye systemi , 12 : 59 – 60 .
   Google Scholar
• DIKIN , L. L . December 1991 . The Convergence of Dual Variables. Technical report , December , Irkutsk : Siberian Energy Institute .
   Google Scholar
• FREUND , R. M . 1991 . Math. prog , 51 : 203 – 222 .
   Web of Science ®Google Scholar
• FREUND , R. M and MIZUNO , S . 1996 . Optima , 51 : 1 – 9 .
   Google Scholar
• FREUND , R. M and NUNEZ , M . March 1996 . Conditions, Measures and properties of the Central Trajectory of Linear Program , Working Paper 3889-96, MSA March , MIT Sloan School .
   Google Scholar
• GONZAGA , C. C . September 1990 . Convergence of the Large Step Primal Affine Scaling Algorithm for Primal Non Degenerate Linear Program , Technical Report ES-230/90 September , Rio de Janeiro : Department of Systems Engineering and Computer Science, COPPE, Federal University of Rio de Janeiro .
   Google Scholar
• JANSEN , B , ROOS , C and TERLAKY , T . 1995 . A Short Survey on Ten Years of Interior Point Methods , Report 95-45 Delft : Delft University of Technology .
   Google Scholar
• KARMARKAR , N . 1984 . Combinatorica , 4 : 373 – 395 .
   Web of Science ®Google Scholar
• KHACHIYAN , L. G . 1979 . Dokl. Akad. Nuk, SSSR , 244 : 1093 – 1096 .
   Google Scholar
• KHACHIYAN , L. G . 1980 . USSR Comput, Math. Math. Phys , 20 : 53 – 72 .
   Google Scholar
• KLEE , V and MINTY , G . 1972 . “ How good is the simplex algorithm? ” . In Inequality III , Edited by: Shisha , O . 159 – 175 . New York : Academic Press .
   Google Scholar
• KOJIMA , M , MEGIDDO , N and MIZUNO , S . 1993 . Math. Prog , 61 : 263 – 280 .
   Web of Science ®Google Scholar
• KOJIMA , M , MEGIDDO , N and YE , Y . 1992 . Math. Prog , 54 : 267 – 279 .
   Web of Science ®Google Scholar
• KOJIMA , M , MIZUNO , S and YOSHISE , A . 1989 . “ A primal-dual interior point algorithm for linear programming ” . In Progress in Mathematical Programming , Edited by: Megiddo , N . 29 – 47 . New York : Springer-Verlag .
   Google Scholar
• MIZUNO , S , MEGIDDO , N and TSUCHIYA , T . 1996 . J. Complex , 12 : 474 – 479 .
   Web of Science ®Google Scholar
• LUSTIG , I. J , MARSTEN , R. E and SHANO , D. F . 1989 . Lin. Algebra Appl , 152
   Google Scholar
• LUSTIG , I. J , MARSTEN , R. E and SHANO , D. F . 1990 . On Implementing Mehrotra's Predictor-Corrector Interior Point Methods for Linear programming , Technical Report, SOR 90-03 Princeton : Department of Civil Engineering and Operations Research, Princeton University .
   Google Scholar
• LUSTIG , I. J , MARSTEN , R. E and SHANO , D. F . Interior-point methods: computational state of the art . ORSA J. Comput , 6 1 – 14 .
   Google Scholar
• MCSHANE , K. A , MONMA , C. L and SHANO , D. F . 1989 . ORSA J. Comput , 1 : 70 – 80 .
   Google Scholar
• MEGIDDO , N . 1989 . “ Pathways to the optimal set in linear programming ” . In Progress in Mathematical Programming , Edited by: Megiddo , N . New York : Springer-Verlag .
   Google Scholar
• MEGIDDO , N and SHUB , M . 1989 . Math. Op. Res , 14 : 97 – 114 .
   Web of Science ®Google Scholar
• MEHROTRA , S . 1992 . SIAM J. Opt , 2 : 575 – 601 .
   Web of Science ®Google Scholar
• MIZUNO , S . 1994 . Math. Prog , 67 : 109 – 119 . 1994
   Web of Science ®Google Scholar
• MIZUNO , S . 1996 . “ Infeasible interior point algorithms ” . In Interior Point Methods in Mathematical Programming , Edited by: Terlaky , T . Dordrecht : Kluwer .
   Google Scholar
• MIZUNO , S , KOJIMA , M and TODD , M. J . 1995 . SIAM J. Opt , 5
   Web of Science ®Google Scholar
• MONMA , C. L and MORTON , A. J . 1987 . Op Res. Lett , 6 : 261 – 267 .
   Web of Science ®Google Scholar
• MONTERIO , R. D. C , ADLER , I and RESNDE , M. G. C . 1990 . Math. Op. Res , 15 : 191 – 214 .
   Web of Science ®Google Scholar
• MURTACH , B. A and SAUNDERS , M. A . 1978 . Math. Prog , 14 : 41 – 72 .
   Web of Science ®Google Scholar
• RENEGAR , J . 1995 . Math. Prog , 70 : 279 – 351 .
   Web of Science ®Google Scholar
• SAIGAL , R . 1995 . Linear Programming: A Modern Integrated Analysis , Boston : Kluwer .
   Google Scholar
• SINGH , J. N and SINGH , D . 1994 . Int, J. Math. Ed. Sci. Tech , 25 : 333 – 341 .
   Google Scholar
• SINGH , J. N , SINGH , D and SHASHI , R . 1995 . J. Inf. Opt. Sci , 16 : 585 – 591 .
   Google Scholar
• SINGH , J. N . Math. Comp. Ed , 31 167 – 175 .
   Google Scholar
• SINGH , J. N . Some remarks on the construction of Central path for linear programming . 6th SIAM Conference on Optimization . May 10–12 , Atlanta, GA, USA.
   Google Scholar
• SINGH , J. N , SHAKIL , M and SINGH , D . 2001 . PNG J. Math., Comput. Ed , 6
   Google Scholar
• TODD , M. J . 1996 . Math. Prog , 76 : 3 – 45 .
   Web of Science ®Google Scholar
• TSENG , P and LUO , Z. Q . 1992 . Math. Prog , 56 : 301 – 319 .
   Web of Science ®Google Scholar
• TSUCHIYA , T . 1991 . Math. Prog , 52 : 377 – 404 .
   Web of Science ®Google Scholar
• TSUCHIYA , T . 1992 . Math. Op. Res , 17 : 527 – 557 .
   Web of Science ®Google Scholar
• TSUCHIYA , T . 1996 . “ Affine-scaling algorithm ” . In Interior Point Methods in Mathematical Programming , Edited by: Terlaky . Dordrecht : Kluwer .
   Google Scholar
• TSUCHIYA , T and MAURAMATU , M . 1995 . SIAM J. Opt , 5 : 525 – 551 .
   Web of Science ®Google Scholar
• VANDERBEI , R. J and LAGARIAS , J. C . 1990 . Contemp. Math , 144
   Google Scholar
• VANDERBEI , R. J , LAGARIAS , J. C , MEKETON , M. S and FREEDMAN , B. A . 1986 . Algorithmica , 1 : 395 – 907 .
   Web of Science ®Google Scholar
• VANDERBEI , R. J . 1996 . Linear Programming: Foundations and Extensions , Dordrecht : Kluwer .
   Google Scholar
• VAVASIS , S and YE , Y . 1996 . Math. Prog , 74 : 79 – 120 .
   Web of Science ®Google Scholar
• XU , X , HUNG , P. F and YE , Y . 1996 . Ann. Op. Res , 62 : 151 – 171 .
   Web of Science ®Google Scholar
• YE , Y . 1988 . Bi-matrix Equilibrium Points and Potential Functions, Linear Programming , Working Paper Series 88-16 Iowa City : Department of Management Sciences, University of Iowa .
   Google Scholar
• YE , Y . 1991 . Math. Prog , 50 : 239 – 258 .
   Web of Science ®Google Scholar
• YE , Y , TODD , M. J and MIZUNO , S . 1994 . Math. Op. Res , 19 : 53 – 67 .
   Web of Science ®Google Scholar
• ARSHAM , H . 1977 . SIAM Rev. , 39 : 736 – 744 .
   Web of Science ®Google Scholar
• ADLER , I , KARMARKAR , N , RESENDE , M. G. C and VEIGA , G . 1989 . Math. Prog , 44 : 297 – 336 .
   Web of Science ®Google Scholar
• ADLER , I , KARMARKAR , N , RESENDE , M. G. C and VEIGA , G . 1989 . ORSA J. Comput , 1 : 89 – 106 .
   Google Scholar
• ANDERSEN , E , GONDZIO , J , MESZAROS , C and XU , X . 1996 . “ Implementation of interior-point methods for large scale linear programming ” . In Interior Point methods in Mathematical Programming , Edited by: Terlaky , T . Dordrecht : Kluwer .
   Google Scholar
• AMSTREICHER , K. M . 1996 . “ Potential reduction methods ” . In Interior Point methods in Mathematical Programming , Edited by: Terlaky , T . Dordrecht : Kluwer .
   Google Scholar
• BARNERS , E. R . 1986 . Math. Prog , 36 : 174 – 182 .
   Web of Science ®Google Scholar