The design and application of IPMLO. A FORTRAN library for linear optimization with interior point methods
RAIRO - Operations Research - Recherche Opérationnelle, Tome 28 (1994) no. 1, pp. 37-56. 
@article{RO_1994__28_1_37_0,
     author = {Gondzio, J. and Tachat, D.},
     title = {The design and application of {IPMLO.} {A} {FORTRAN} library for linear optimization with interior point methods},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {37--56},
     publisher = {EDP-Sciences},
     volume = {28},
     number = {1},
     year = {1994},
     mrnumber = {1269100},
     zbl = {0860.90085},
     language = {en},
     url = {http://archive.numdam.org/item/RO_1994__28_1_37_0/}
}
TY  - JOUR
AU  - Gondzio, J.
AU  - Tachat, D.
TI  - The design and application of IPMLO. A FORTRAN library for linear optimization with interior point methods
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 1994
SP  - 37
EP  - 56
VL  - 28
IS  - 1
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/RO_1994__28_1_37_0/
LA  - en
ID  - RO_1994__28_1_37_0
ER  - 
%0 Journal Article
%A Gondzio, J.
%A Tachat, D.
%T The design and application of IPMLO. A FORTRAN library for linear optimization with interior point methods
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 1994
%P 37-56
%V 28
%N 1
%I EDP-Sciences
%U http://archive.numdam.org/item/RO_1994__28_1_37_0/
%G en
%F RO_1994__28_1_37_0
Gondzio, J.; Tachat, D. The design and application of IPMLO. A FORTRAN library for linear optimization with interior point methods. RAIRO - Operations Research - Recherche Opérationnelle, Tome 28 (1994) no. 1, pp. 37-56. http://archive.numdam.org/item/RO_1994__28_1_37_0/

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

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 | Zbl

R. Bixby, Implementing the Simplex Method: the Initial Basis, O.R.S.A. Journal on Computing, 1992, 4, No. 3, pp. 267-284. | MR | Zbl

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

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

R. W. Cottle, Manifestations of the Schur Complement, Linear Algebra and its Applications, 1974, 8, pp. 189-211. | MR | Zbl

L. S. Duff, A. M. Erisman and J. K. Reid, Direct methods for sparse matrices. Oxford University Press, New York, 1989. | MR | Zbl

A. V. Fiacco and G. P. Mccormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley, NewYork, 1968. | MR | Zbl

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

D. M. Gay, Electronic Mail Distribution of Linear Programming Test Problems, Mathematical Programming Society COAL Newsletter, 1985.

A. George and J. W. H. Liu, Computer Solution of Large Sparse Positive Definite Systems, Prentice Inc., Englewood Cliffs, 1981. | MR | Zbl

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

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 | Zbl

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

G. H. Golub and C. F. Van Loan, Matrix Computations, John Hopkins University Press, Baltimore, 1983. | MR | Zbl

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

J. Gondzio, Implementing Cholesky Factorization for Interior Point Methods of Linear Programming, Optimization, 1991, (to appear). | MR | Zbl

J. Gondzio, Splitting Dense Columns of Constraint Matrix in Interior Point Methods for Large Scale Linear Programming, Optimization, 1992, 24, pp. 285-297. | MR | Zbl

W. Hager, Updating the Inverse of a Matrix, S.I.A.M. Review, 1989, 31, No. 2, pp. 221-239. | MR | Zbl

N. K. Karmarkar, A New Polynomial Time Algorithm for Linear Programming, Combinatorica, 1984, 4, pp. 373-395. | MR | Zbl

N. K. Karmarkar, A Talk at the Asilomar Conference on Interior Point Methods, Asilomar, California, U.S.A., 1985.

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 | Zbl

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

A. Lisser and P. Tolla, Variants of Karmarkar's Algorithm, Technical Report 90, LAMSADE, University of Paris Dauphine, March, 1989. | Zbl

I. Lustig, Feasibility Issues in a Primal-Dual Interior Point Method for Linear Programming, Mathematical Programming, 1991, 49, pp. 145-162. | MR | Zbl

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 | Zbl

R. E. Marsten, The Design of XMP Linear Programming Library, A.C.M. Transactions on Mathematical Software, 1981, 7, pp. 481-497.

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

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

N. Megiddo, Pathways to the Optimal Setin Linear Programming, in: N. MEGIDDO Ed., Progress in Mathematical Programming, Springer-Verlag, New York, 1986. | Zbl

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 | Zbl

R. C. Monteiro and I. Adler, Interior Path Following Primal-Dual Algorithms - part I: Linear Programming, Mathematical Programming, 1989, 44, pp. 27-41. | MR | Zbl

B. Murtagh, Advanced Linear Programming, Computation and Practice, McGraw-Hill, New York, 1981. | MR | Zbl

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).

J. K. Reid, A Sparsity Exploiting Variant of the Bartels-Golub Decomposition for linear programming Bases, Mathematical Programming, 1982, 24, pp. 55-69. | MR | Zbl

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).

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.

R. J. Vanderbei, Splitting Dense Columns in Sparse Linear Systems, Linear Algebra and its Applications, 1991, 152, pp. 107-117. | MR | Zbl

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