The trust region affine interior point algorithm for convex and nonconvex quadratic programming
RAIRO - Operations Research - Recherche Opérationnelle, Volume 29 (1995) no. 2, pp. 195-217.
@article{RO_1995__29_2_195_0,
     author = {Bonnans, J. F. and Bouhtou, M.},
     title = {The trust region affine interior point algorithm for convex and nonconvex quadratic programming},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {195--217},
     publisher = {EDP-Sciences},
     volume = {29},
     number = {2},
     year = {1995},
     mrnumber = {1337889},
     zbl = {0835.90061},
     language = {en},
     url = {http://archive.numdam.org/item/RO_1995__29_2_195_0/}
}
TY  - JOUR
AU  - Bonnans, J. F.
AU  - Bouhtou, M.
TI  - The trust region affine interior point algorithm for convex and nonconvex quadratic programming
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 1995
SP  - 195
EP  - 217
VL  - 29
IS  - 2
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/RO_1995__29_2_195_0/
LA  - en
ID  - RO_1995__29_2_195_0
ER  - 
%0 Journal Article
%A Bonnans, J. F.
%A Bouhtou, M.
%T The trust region affine interior point algorithm for convex and nonconvex quadratic programming
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 1995
%P 195-217
%V 29
%N 2
%I EDP-Sciences
%U http://archive.numdam.org/item/RO_1995__29_2_195_0/
%G en
%F RO_1995__29_2_195_0
Bonnans, J. F.; Bouhtou, M. The trust region affine interior point algorithm for convex and nonconvex quadratic programming. RAIRO - Operations Research - Recherche Opérationnelle, Volume 29 (1995) no. 2, pp. 195-217. http://archive.numdam.org/item/RO_1995__29_2_195_0/

1. I. Adler, M. G. C. Resende, G. Veiga, An implementation of Karmarkar's algorithm for linear programming, Math. Programming, 1989, 44, pp. 297-335. | MR | Zbl

2. I. Adler, R. D. C. Monteiro, Limiting behavior of the affine scaling continuous trajectories for linear programming problems, Math. Programming, 1991, 50, pp. 29-51. | MR | Zbl

3. E. R. Barnes, A variation on Karmarkar's algorithm for solving linear programming, Math Programming, 1986, 36, pp. 174-182. | MR | Zbl

4. F. Delebecque, C. Klimann, S. Steer, Basile. Un système de CAO pour l'automatique, Version 3.0. Guide d'utilisation, INRIA, Mars 1989.

5. D. A. Bayer, J. C. Lagarias, The nonlinear geometry of linear programming: I Affine and projective trajectories, Trans, Amer. Math. Soc., 1989, (2), 314, pp. 499-526. | MR | Zbl

6. M. Bouthou, Méthodes de points intérieurs pour l'optimisation des systèmes de grande taille, Thèse de Doctorat, Université Paris Dauphine, 1993.

7. J.-P. Bulteau, J.-P. Vial, A restricted trust region algorithms for unconstrained optimization, Optim. Theory and Appl., 1985, 47, n° 4, pp. 413-435. | MR | Zbl

8. E. Casas, C. Pola, Dealing with degenerated cases in quadratic programs, RAIRO-Operations Research, 1994, 27, n° 4, pp. 401 à 426. | Numdam | MR | Zbl

9. I. I. Dikin, Iterative solutions of problems of linear and quadratic programming, Soviet. Math. Doklady, 1967, 8, pp. 674-675. | Zbl

10. C. C. Gonzaga, L. A. Carlos, A primal affine scaling algorithm for linearly constrained convex programs, Report, Federal University of Rio de Janeiro.

11. C. C. Gonzaga, Convergence of the large step primal affine scaling algorithm for primal non-degenerate linear programs, Tech. Report, Federal University of Rio de Janeiro, Brazil.

12. M. D. Hebden, An algorithm for minimization using exact second derivatives. Atomic Energy Research, Establishment report TP 515, Harwell, England 1973.

13. N. Karmarkar, A new polynomial time algorithm for linear programming, Combinatorica, 1984, 4, pp. 373-395. | MR | Zbl

14. M. Kojima, S. Mizuno, A. Yoshise, AN O (√nL) iteration potential reduction algorithm for linear complementarity problems, Math. Programming, 1991, 50, pp. 331-342. | MR | Zbl

15. O. L. Mangasarian, A simple characterization of solution sets of convex programs, Oper. Res. Lett., 1988, 7, pp. 21-26. | MR | Zbl

16. N. Megiddo, M. Shub, Boundary behavior of interior point algorithms for linear programming, Math. Oper, Res., 1989, 14, pp. 97-146. | MR | Zbl

17. R. D. C. Monteiro, I. Adler, M. G. C. Resende, A polynomial time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extensions, Math. Oper. Res., 1990, 15 (2). | MR | Zbl

18. J. J. Moré, Recent developments in algorithms and software for trust region method, Born 1982, Springer Verlag. | MR | Zbl

19. R. Saigal, A three step quadratically convergent implementation of the primal affine scalling method, Technical Report 93-9, Department of Industrial and Operational Engineering, University of Michigan, Ann-Arbor, MI-48109-2117, USA.

20. J. Sun, A convergence proof of an affine-scaling algorithm for convex quadratic programming without nondegeneracy assumptions, Technical Report, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA, 1990. | Zbl

21. P. Tseng, Z. Q. Luo, On the convergence of the affine scaling algorithm, Technical Report, CICS-P-169, Center for Intelligent Control Systems, Massachusetts Institute of Technology (Cambridge, MA, 1989). | Zbl

22. T. Tsuchiya, Global convergence of the affine scaling methods for degenerate linear programming problem, Math. Programming, 1991, 52, pp. 377-404. | MR | Zbl

23. T. Tsuchiya, Global convergence of the affine scaling algorithm for the primal degenerate strictly convex quadratic programming problems, The Institute of Statistical Mathematics, Tokyo, Japan, Technical report n° 417. | Zbl

24. T. Tsuchiya, M. Muratmatsu, Global convergence of a long-step affine scaling algorithm for degenerate linear programming problems, Research Memorandum 423, the Institute of Statistical Mathematics, 4-6-7 Minami-Azabou, Minoto-Ku, Tokyo 106, Japan, 1992. | Zbl

25. T. Tsuchiya, R. D. C. Monteiro, Superlinear convergence of the affine scaling algorithm, Department of Systems and Industrial Engineering, University of Arizona, Tucson, Technical Report. | Zbl

26. R. J. Vanderbei, S. M. Meketon, B. A. Freedman, A modification of Karmarkar's linear programming algorithm, Algorithmica, 1986, 1, pp. 395-407. | MR | Zbl

27. Y. Ye, E. Tse, An extension of Karmarkar's projective algorithm for convex quadratic programming, Math. Programming, 1989, 44, pp. 157-179. | MR | Zbl

28. Y. Ye, On affine scaling algorithms for nonconvex quadratic programming, Math. Prog., 1992, 56, 3, pp. 285-301. | MR | Zbl