Inverse barrier methods for linear programming
RAIRO - Operations Research - Recherche Opérationnelle, Tome 28 (1994) no. 2, pp. 135-163. 
@article{RO_1994__28_2_135_0,
     author = {Hertog, D. Den and Roos, C. and Terlaky, T.},
     title = {Inverse barrier methods for linear programming},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {135--163},
     publisher = {EDP-Sciences},
     volume = {28},
     number = {2},
     year = {1994},
     mrnumber = {1277325},
     zbl = {0857.90080},
     language = {en},
     url = {http://www.numdam.org/item/RO_1994__28_2_135_0/}
}
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
SP  - 135
EP  - 163
VL  - 28
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/RO_1994__28_2_135_0/
LA  - en
ID  - RO_1994__28_2_135_0
ER  - 
%0 Journal Article
%A Hertog, D. Den
%A Roos, C.
%A Terlaky, T.
%T Inverse barrier methods for linear programming
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 1994
%P 135-163
%V 28
%N 2
%I EDP-Sciences
%U http://www.numdam.org/item/RO_1994__28_2_135_0/
%G en
%F RO_1994__28_2_135_0
Hertog, D. Den; Roos, C.; Terlaky, T. Inverse barrier methods for linear programming. RAIRO - Operations Research - Recherche Opérationnelle, Tome 28 (1994) no. 2, pp. 135-163. http://www.numdam.org/item/RO_1994__28_2_135_0/

1. C. W. Carroll, The Created Response Surface Technique for Optimizing Nonlinear Restrainecl Systems, Operations Research, 1961, 9, pp. 169-184. | Zbl

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. | Zbl

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. | Zbl

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. | Zbl

6. R. Fletcher and A. P. Mccann, Acceleration Techniques for Nonlinear Programming, In Optimization, R. Fletcher ed., Academie Press, London, 1969, pp. 203-214. | Zbl

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. | MR | Zbl

9. C. C. Gonzaga, Large-Steps Path-Following Methods for Linear Programming: Barrier Function Method, SIAM Journal on Optimization, 1991, 1, pp. 268-279. | MR | Zbl

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. | MR | Zbl

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

12. J. Kowalk, Nonlinear Programming Procedures and Design Optimization, Acta Polyntech. Scand., 1966, 13, Trondheim. | MR

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. | MR | Zbl

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. | MR | Zbl

16. R. A. Polyak, Modified Banier Functions (theory and methods), Mathematical Programming, 1992, 54, pp. 174-222. | Zbl

17. J. Renegar, A Polynomial-Time Algorithm, Based on Newton's Method, for Linear Programming, Mathematical Programming, 1988, 40, pp.59-93. | MR | Zbl

18. C. Roos and J.-Ph. Vial, A Polynomial Method of Approximate Centers for Linear Programming, Mathematical Programming, 1992, 54, pp.295-305. | MR | Zbl

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. | Zbl

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. | Zbl

21. D. J. White, Linear Programming and Huard's Method of Centres, Working, Paper, Universities of Manchester and Virginia, United Kingdom, 1989.