The design and application of IPMLO. A FORTRAN library for linear optimization with interior point methods

 Access to full text

 Full (PDF)

1. 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. Zbl0752.90043
2. 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. Zbl0682.90061MR1028226
3. R. BIXBY, Implementing the Simplex Method: the Initial Basis, O.R.S.A. Journal on Computing, 1992, 4, No. 3, pp. 267-284. Zbl0759.90063MR1181652
4. 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. MR1021068
5. 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. Zbl0757.90051
6. R. W. COTTLE, Manifestations of the Schur Complement, Linear Algebra and its Applications, 1974, 8, pp. 189-211. Zbl0284.15005MR354727
7. L. S. DUFF, A. M. ERISMAN and J. K. REID, Direct methods for sparse matrices. Oxford University Press, New York, 1989. Zbl0666.65024MR1029273
8. A. V. FIACCO and G. P. MCCORMICK, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley, NewYork, 1968. Zbl0563.90068MR243831
9. 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. Zbl0814.90075
10. D. M. GAY, Electronic Mail Distribution of Linear Programming Test Problems, Mathematical Programming Society COAL Newsletter, 1985. 
11. A. GEORGE and J. W. H. LIU, Computer Solution of Large Sparse Positive Definite Systems, Prentice Inc., Englewood Cliffs, 1981. Zbl0516.65010MR646786
12. 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. Zbl0411.68029
13. 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. Zbl0624.90062MR866988
14. 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. MR1105101
15. G. H. GOLUB and C. F. VAN LOAN, Matrix Computations, John Hopkins University Press, Baltimore, 1983. Zbl0733.65016MR733103
16. 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). Zbl0806.90083
17. J. GONDZIO, Implementing Cholesky Factorization for Interior Point Methods of Linear Programming, Optimization, 1991, (to appear). Zbl0819.65097MR1275552
18. J. GONDZIO, Splitting Dense Columns of Constraint Matrix in Interior Point Methods for Large Scale Linear Programming, Optimization, 1992, 24, pp. 285-297. Zbl0814.65056MR1247637
19. W. HAGER, Updating the Inverse of a Matrix, S.I.A.M. Review, 1989, 31, No. 2, pp. 221-239. Zbl0671.65018MR997457
20. N. K. KARMARKAR, A New Polynomial Time Algorithm for Linear Programming, Combinatorica, 1984, 4, pp. 373-395. Zbl0557.90065MR779900
21. N. K. KARMARKAR, A Talk at the Asilomar Conference on Interior Point Methods, Asilomar, California, U.S.A., 1985. 
22. 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. Zbl0739.90042MR1148186
23. 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. Zbl0708.90049
24. A. LISSER and P. TOLLA, Variants of Karmarkar's Algorithm, Technical Report 90, LAMSADE, University of Paris Dauphine, March, 1989. Zbl0695.90058
25. I. LUSTIG, Feasibility Issues in a Primal-Dual Interior Point Method for Linear Programming, Mathematical Programming, 1991, 49, pp. 145-162. Zbl0726.90050MR1087451
26. 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. Zbl0731.65049MR1107553
27. R. E. MARSTEN, The Design of XMP Linear Programming Library, A.C.M. Transactions on Mathematical Software, 1981, 7, pp. 481-497. 
28. 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, Zbl0798.90100
29. 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. Zbl0752.90047
30. N. MEGIDDO, Pathways to the Optimal Setin Linear Programming, in: N. MEGIDDO Ed., Progress in Mathematical Programming, Springer-Verlag, New York, 1986. Zbl0687.90056
31. 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. Zbl0627.90065MR926036
32. R. C. MONTEIRO and I. ADLER, Interior Path Following Primal-Dual Algorithms - part I: Linear Programming, Mathematical Programming, 1989, 44, pp. 27-41. Zbl0676.90038MR999721
33. B. MURTAGH, Advanced Linear Programming, Computation and Practice, McGraw-Hill, New York, 1981. Zbl0525.90062MR609151
34. 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). 
35. J. K. REID, A Sparsity Exploiting Variant of the Bartels-Golub Decomposition for linear programming Bases, Mathematical Programming, 1982, 24, pp. 55-69. Zbl0492.90050MR667939
36. 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). 
37. 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. 
38. R. J. VANDERBEI, Splitting Dense Columns in Sparse Linear Systems, Linear Algebra and its Applications, 1991, 152, pp. 107-117. Zbl0727.65034MR1107547
39. 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. Zbl0683.90046