Inverse barrier methods for linear programming
D. Den Hertog; C. Roos; T. Terlaky
RAIRO - Operations Research - Recherche Opérationnelle (1994)
- Volume: 28, Issue: 2, page 135-163
- ISSN: 0399-0559
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topHertog, D. Den, Roos, C., and Terlaky, T.. "Inverse barrier methods for linear programming." RAIRO - Operations Research - Recherche Opérationnelle 28.2 (1994): 135-163. <http://eudml.org/doc/105079>.
@article{Hertog1994,
author = {Hertog, D. Den, Roos, C., Terlaky, T.},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {interior point methods; logarithmic barrier method; inverse barrier methods},
language = {eng},
number = {2},
pages = {135-163},
publisher = {EDP-Sciences},
title = {Inverse barrier methods for linear programming},
url = {http://eudml.org/doc/105079},
volume = {28},
year = {1994},
}
TY - JOUR
AU - Hertog, D. Den
AU - Roos, C.
AU - Terlaky, T.
TI - Inverse barrier methods for linear programming
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 1994
PB - EDP-Sciences
VL - 28
IS - 2
SP - 135
EP - 163
LA - eng
KW - interior point methods; logarithmic barrier method; inverse barrier methods
UR - http://eudml.org/doc/105079
ER -
References
top- 1. C. W. CARROLL, The Created Response Surface Technique for Optimizing Nonlinear Restrainecl Systems, Operations Research, 1961, 9, pp. 169-184. Zbl0111.17004
- 2. D. DEN HERTOG, C. ROOS and T. TERLAKY, A potential Reduction Variant of Renegar's Short-Step Path-Following Method for Linear Programming, Linear Algebra and Its Applications, 1991, 68, pp. 43-68. Zbl0734.65050
- 3. D. DEN HERTOG, C. ROOS and J.-Ph. VIAL, A √n Complexity Reduction for Long Step Path-following Methods, SIAM Journal on Optimization, 1992, 2, pp. 71-87. Zbl0763.90064
- 4. J. R. ERIKSSON, An Iterative Primal-Dual Algorithm for Linear Programming, Report LiTH-MAT-R-1985-10, 1985, Department of Mathematics, Linköping University, Linköping, Sweden.
- 5. A. V. FIACCO and G. P. MCCORMICK, Nonlinear Programming, Sequential Unconstrained Minimization Techniques, Wiley and Sons, New York, 1968. Zbl0563.90068
- 6. R. FLETCHER and A. P. MCCANN, Acceleration Techniques for Nonlinear Programming, In Optimization, R. Fletcher ed., Academie Press, London, 1969, pp. 203-214. Zbl0194.47704
- 7. R. FRISCH, The Logarithmic Potential Method for Solving Linear Programming Problems, Memorandum, University Institute of Economies, Oslo, 1955.
- 8. C. C. GONZAGA, An Algorithm for Solving Linear Programming Problems in O(n3 L) Operations, In Progress in Mathematical Programming, Interior Point and Related Methods, pp. 1-28, N. Megiddo ed., Springer Verlag, New York, 1989. Zbl0691.90053MR982713
- 9. C. C. GONZAGA, Large-Steps Path-Following Methods for Linear Programming: Barrier Function Method, SIAM Journal on Optimization, 1991, 1, pp. 268-279. Zbl0754.90035MR1098430
- 10. P. HUARD, Resolution of Mathematical Programming with Nonlinear Constraints by the Methods of Centres, In Nonlinear Programming, J. Abadie éd., North-Holland Publishing Company, Amsterdam, Holland, 1989, pp. 207-219. Zbl0157.49701MR216865
- 11. N. KARMARKAR, A New Polynomial-Time Algorithm for Linear Programming, Comhinatorica, 4, 1984, pp. 373-395. Zbl0557.90065MR779900
- 12. J. KOWALK, Nonlinear Programming Procedures and Design Optimization, Acta Polyntech. Scand., 1966, 13, Trondheim. MR207398
- 13. G. P. MCCORMICK, W. C. MYLANDER and A. V. FIACCO, Computer Program Implementing the Sequential Unconstrained Minimization Technique for Nonlinear Programming, Technical Paper RAC-TP-151, Research Analysis Corporation, McLean, 1965.
- 14. N. MEGIDDO, Pathways to the Optimal Set in Linear Programming, In Progress in Mathematical Programming, Interior Point and Related Methods, pp. 131-158, N. Megiddo ed., Springer Verlag, New York, 1989. Zbl0687.90056MR982720
- 15. R. D. C. MONTEIRO and I. ADLER, Interior Path Following Prima-Dual Algorithms, Part I: Linear Programming, Mathematical Programming, 1989, 44, pp. 27-41. Zbl0676.90038MR999721
- 16. R. A. POLYAK, Modified Banier Functions (theory and methods), Mathematical Programming, 1992, 54, pp. 174-222. Zbl0756.90085
- 17. J. RENEGAR, A Polynomial-Time Algorithm, Based on Newton's Method, for Linear Programming, Mathematical Programming, 1988, 40, pp.59-93. Zbl0654.90050MR923697
- 18. C. Roos and J.-Ph. VIAL, A Polynomial Method of Approximate Centers for Linear Programming, Mathematical Programming, 1992, 54, pp.295-305. Zbl0771.90067MR1159483
- 19. C. Roos and J.-Ph. VIAL, Long Steps with the Logarithmic Penalty Banier Function in Linear Programming, In Economic Decision-Making: Games, Economics and Optimization, dedicated to Jacques H. Drèze, edited by J. Gabszevwicz, J.-F. Richard and L. Wolsey, Elsevier Sciences Publisher B. V., 1989, pp. 433-441. Zbl0709.90076
- 20. A. TAMURA, H. TAKEHARA, K. FUKUDA, S. FUJISHIGE and S. KOJIMA, A Dual Primal Simplex Methods for Linear Programming, Journal of the Operations Research Society of Japan, 1988, 31, pp.413-429. Zbl0658.90062
- 21. D. J. WHITE, Linear Programming and Huard's Method of Centres, Working, Paper, Universities of Manchester and Virginia, United Kingdom, 1989.
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