EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 28 / No 1 (1994) RAIRO-Oper. Res., 28 1 (1994) 37-56 References
Free Access
Issue
RAIRO-Oper. Res.
Volume 28, Number 1, 1994
Page(s) 37 - 56
DOI https://doi.org/10.1051/ro/1994280100371
Published online 06 February 2017
  • I. ADLER, N. KARMARKAR, M. G. C. RESENDE and G. VEIGA, Data Structures and Programming Techniques for the Implementation of Karmarkar's Algorithm, O.R.S.A. Journal on Computing, 1989, a, 1, No. 2, pp. 84-106. [Zbl: 0752.90043] [Google Scholar]
  • I. ADLER, N. KARMARKA, M. G. C. RESENDE and G. VEIGA, An Implementaiton of Karmarkar's Algorithm for Linear Programming, Mathematical Programming, 1989, b, 44, pp. 297-335. [MR: 1028226] [Zbl: 0682.90061] [Google Scholar]
  • R. BIXBY, Implementing the Simplex Method: the Initial Basis, O.R.S.A. Journal on Computing, 1992, 4, No. 3, pp. 267-284. [MR: 1181652] [Zbl: 0759.90063] [Google Scholar]
  • Y.-C. CHENG, D. J. Jr. HOUCK, J.-M. LIU, M. S. MEKETON, L. SLUTSMAN, R. J. VANDERBEI and P. WANG, The AT&T KORBX System, AT&T Technical Journal, 1989, May/June, pp. 7-19. [MR: 1021068] [Google Scholar]
  • I. C. CHOI, C. L. MONMA and D. F. SHANNO, Further Development of a Primal-Dual Interior Point Method, O.R.S.A. Journal on Computing, 1990, 2, pp. 304-311. [Zbl: 0757.90051] [Google Scholar]
  • R. W. COTTLE, Manifestations of the Schur Complement, Linear Algebra and its Applications, 1974, 8, pp. 189-211. [MR: 354727] [Zbl: 0284.15005] [Google Scholar]
  • L. S. DUFF, A. M. ERISMAN and J. K. REID, Direct methods for sparse matrices. Oxford University Press, New York, 1989. [MR: 1029273] [Zbl: 0666.65024] [Google Scholar]
  • A. V. FIACCO and G. P. MCCORMICK, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley, NewYork, 1968. [MR: 243831] [Zbl: 0563.90068] [Google Scholar]
  • J. J. H. FORREST and J. A. TOMLIN, Implementing the Simplex Method for the Optimization Subroutine Library, I.B.M. Systems Journal, 1991, 31, No. 2, pp. 11-25. [Zbl: 0814.90075] [Google Scholar]
  • D. M. GAY, Electronic Mail Distribution of Linear Programming Test Problems, Mathematical Programming Society COAL Newsletter, 1985. [Google Scholar]
  • A. GEORGE and J. W. H. LIU, Computer Solution of Large Sparse Positive Definite Systems, Prentice Inc., Englewood Cliffs, 1981. [MR: 646786] [Zbl: 0516.65010] [Google Scholar]
  • P. E. GILL, W. MURRAY, S. M. PICKEN and M. H. WRIGHT, The Design and Strucutre of a FORTRAN Program Library for Optimization. A.C.M. Transactions on Mathematical Software, 1979, 5, No. 3, pp. 259-283. [Zbl: 0411.68029] [Google Scholar]
  • P. E. GILL, W. MURRAY, M. A. SAUNDERS, J. A. TOMLIN and M. H. WRIGHT, On Projected Newton Barrier Methods for Linear Programming and an Equivalence to Karmarkar's Projective Method, Mathematical Programming, 1986, 36, pp. 183-209. [MR: 866988] [Zbl: 0624.90062] [Google Scholar]
  • D. GOLDFARB and M. J. TODD, Linear Programming, in: G. L. NEMHAUSER, A. H. G. RINNOOY KAN and M. J. TODD Eds., Optimization, North Holland, Amsterdam, 1989. [MR: 1105101] [Google Scholar]
  • G. H. GOLUB and C. F. VAN LOAN, Matrix Computations, John Hopkins University Press, Baltimore, 1983. [MR: 733103] [Zbl: 0733.65016] [Google Scholar]
  • J. GONDZIO, On Exploiting Original Problem Data in the Inverse Representation of the Linear Programming bases, O.R.S.A. Journal on Computing, 1990 (to appear). [Zbl: 0806.90083] [Google Scholar]
  • J. GONDZIO, Implementing Cholesky Factorization for Interior Point Methods of Linear Programming, Optimization, 1991, (to appear). [MR: 1275552] [Zbl: 0819.65097] [Google Scholar]
  • J. GONDZIO, Splitting Dense Columns of Constraint Matrix in Interior Point Methods for Large Scale Linear Programming, Optimization, 1992, 24, pp. 285-297. [MR: 1247637] [Zbl: 0814.65056] [Google Scholar]
  • W. HAGER, Updating the Inverse of a Matrix, S.I.A.M. Review, 1989, 31, No. 2, pp. 221-239. [MR: 997457] [Zbl: 0671.65018] [Google Scholar]
  • N. K. KARMARKAR, A New Polynomial Time Algorithm for Linear Programming, Combinatorica, 1984, 4, pp. 373-395. [MR: 779900] [Zbl: 0557.90065] [Google Scholar]
  • N. K. KARMARKAR, A Talk at the Asilomar Conference on Interior Point Methods, Asilomar, California, U.S.A., 1985. [Google Scholar]
  • N. K. KARMARKAR and K. G. RAMAKRISHNAN, Computational Results of an Interior Point Algorithm for Large Scale Linear Programming, Mathematical Programming, 1991, 52, pp, 555-586. [MR: 1148186] [Zbl: 0739.90042] [Google Scholar]
  • M. KOJIMA, S. MIZUNO and A. YOSHISE, A Primal-Dual Interior Point Algorithm for Linear Programming, in: N. MEGIDDO Ed., Progress in Mathematical Programming, Springer-Verlag, New York, 1986. [Zbl: 0708.90049] [Google Scholar]
  • A. LISSER and P. TOLLA, Variants of Karmarkar's Algorithm, Technical Report 90, LAMSADE, University of Paris Dauphine, March, 1989. [Zbl: 0695.90058] [Google Scholar]
  • I. LUSTIG, Feasibility Issues in a Primal-Dual Interior Point Method for Linear Programming, Mathematical Programming, 1991, 49, pp. 145-162. [MR: 1087451] [Zbl: 0726.90050] [Google Scholar]
  • I. LUSTIG, R. E. MARSTEN and D. F. SHANNO, Computational Experience with a Primal-Dual Interior Point Method for Linear Programming, Linear Algebra and its Applications, 1991, 152, pp. 191-222. [MR: 1107553] [Zbl: 0731.65049] [Google Scholar]
  • R. E. MARSTEN, The Design of XMP Linear Programming Library, A.C.M. Transactions on Mathematical Software, 1981, 7, pp. 481-497. [Google Scholar]
  • R. E. MARSTEN, R. SUBMARANIAN, M. SALTZMAN, I. LUSTIG and D. SHANNO, Interior Point Methods for Linear Programming: Just Call Newton, Lagrange and Fiacco and McCormick, Interfaces, 1990, 20, pp. 105-116, [Zbl: 0798.90100] [Google Scholar]
  • K. A. MCSHANE, C. L. MONMA and D. F. SHANNO, An Implementation of a PrimalDual Interior Point Method for Linear Programming, O.R.S.A. Journal on Computing, 1989, 1, pp. 70-83. [Zbl: 0752.90047] [Google Scholar]
  • N. MEGIDDO, Pathways to the Optimal Setin Linear Programming, in: N. MEGIDDO Ed., Progress in Mathematical Programming, Springer-Verlag, New York, 1986. [Zbl: 0687.90056] [Google Scholar]
  • C. L. MONMA and A. J. MORTON, Computational Experience with a Dual Affine Variant of Karmarkar's Method for Linear Programming, Operations Research Letters, 1987, 6, pp. 261-267. [MR: 926036] [Zbl: 0627.90065] [Google Scholar]
  • R. C. MONTEIRO and I. ADLER, Interior Path Following Primal-Dual Algorithms - part I: Linear Programming, Mathematical Programming, 1989, 44, pp. 27-41. [MR: 999721] [Zbl: 0676.90038] [Google Scholar]
  • B. MURTAGH, Advanced Linear Programming, Computation and Practice, McGraw-Hill, New York, 1981. [MR: 609151] [Zbl: 0525.90062] [Google Scholar]
  • B. MURTAGH and M. A. SAUNDERS, MINOS 5.1 User's guide, Technical Report SOL 83-20R, Department of Operations Research, Stanford University, Stanford, California, 1983 (revised 1987). [Google Scholar]
  • J. K. REID, A Sparsity Exploiting Variant of the Bartels-Golub Decomposition for linear programming Bases, Mathematical Programming, 1982, 24, pp. 55-69. [MR: 667939] [Zbl: 0492.90050] [Google Scholar]
  • D. TACHAT, Interior Point Methods for Linear Programming: Computing Exact and Approximate Projections, Ph. D. Thesis, LAMSADE, University of Paris-Dauphine, Paris, 1991 (in French). [Google Scholar]
  • P. TOLLA, Improvement of the Efficiency of Karmarkar's Algorithm for Linear Programs with Upper Bounded Variables, Technical Report 82, LAMSADE, University of Paris-Dauphine, Paris, November, 1987. [Google Scholar]
  • R. J. VANDERBEI, Splitting Dense Columns in Sparse Linear Systems, Linear Algebra and its Applications, 1991, 152, pp. 107-117. [MR: 1107547] [Zbl: 0727.65034] [Google Scholar]
  • J.-P. VIAL, A Unified Approach to Projective Algorithms for Linear Programming, Technical Report, Département d'Economie commerciale et industrielle, University of Geneva, Geneva, September 1987. [Zbl: 0683.90046] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.