On the central path for nonlinear semidefinite programming
RAIRO - Operations Research - Recherche Opérationnelle, Tome 34 (2000) no. 3, pp. 331-345. 
@article{RO_2000__34_3_331_0,
     author = {Gra\~na Drummond, L. M. and Iusem, Alfredo Noel and Svaiter, B. F.},
     title = {On the central path for nonlinear semidefinite programming},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {331--345},
     publisher = {EDP-Sciences},
     volume = {34},
     number = {3},
     year = {2000},
     mrnumber = {1786466},
     zbl = {0971.90088},
     language = {en},
     url = {http://www.numdam.org/item/RO_2000__34_3_331_0/}
}
TY  - JOUR
AU  - Graña Drummond, L. M.
AU  - Iusem, Alfredo Noel
AU  - Svaiter, B. F.
TI  - On the central path for nonlinear semidefinite programming
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2000
SP  - 331
EP  - 345
VL  - 34
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/RO_2000__34_3_331_0/
LA  - en
ID  - RO_2000__34_3_331_0
ER  - 
%0 Journal Article
%A Graña Drummond, L. M.
%A Iusem, Alfredo Noel
%A Svaiter, B. F.
%T On the central path for nonlinear semidefinite programming
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2000
%P 331-345
%V 34
%N 3
%I EDP-Sciences
%U http://www.numdam.org/item/RO_2000__34_3_331_0/
%G en
%F RO_2000__34_3_331_0
Graña Drummond, L. M.; Iusem, Alfredo Noel; Svaiter, B. F. On the central path for nonlinear semidefinite programming. RAIRO - Operations Research - Recherche Opérationnelle, Tome 34 (2000) no. 3, pp. 331-345. http://www.numdam.org/item/RO_2000__34_3_331_0/

1. F. Alizadeh, J.-P. A. Haeberly and M. L. Overton, Complementarity and nondegeneracy in semidefinite programming. Math. Programming 77 (1997) 111-128. | MR | Zbl

2. D. Bayer and J. C. Lagarias, The non-linear geometry of linear programming. AT & Bell Laboratories, Murray Hill, NJ (1986), preprint. | Zbl

3. A. Fiacco and G. P. Mccormik, Nonlinear Programming: Sequential Unconstrained Techniques. Classics in Applied Mathematics, SIAM Publications, Philadelphia (1990). | MR | Zbl

4. D. Goldfarb and K. Sheinberg, Interior point trajectories in semidefinite programming (1996) preprint. | Zbl

5. L. M. Graña Drummond, Classical and generalized central paths with algorithmic applications in linear programming. Ph. D. Thesis, Instituto deMatemâtica Pura e Aplicada, Rio de Janeiro, Brazil (1997).

6. L. M. Graña Drummond and A. N. Iusem, Welldefinedness and limiting behavior of the central path. Computational and Applied Mathematics (accepted). | Zbl

7. L. M. Graña Drummond and A. N. Iusem On the central path for semidefinite programming. Tecnhical Report ES-473/98, Programa de Engenharia de Sistemas e Computação, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil (1998).

8. L. M. Graña Drummond and B. F. Svaiter, On well definedness of the central path. J. Optim. Theory Appl. 102 (1999) 223-237. | MR | Zbl

9. A. N. Iusem, B. F. Svaiter and J. X. Da Cruz Neto, Central paths, generalized proximal point methods and Cauchy trajectories in Riemann manifolds. SIAM J. Control Optim. 37 (1999) 566-588. | MR | Zbl

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

11. L. G. Khachiyan, A polynomial algorithm for linear programming, Soviet Math. Dokl 20 (1979) 191-194. | Zbl

11. M. Kojima, S. Mizuno and T. Toma, Limiting behavior of trajectories by a continuation method for complementary problems. Math. Oper. Res. 15 (1990) 662-675. | MR | Zbl

13. M. Kojima, S. Shindoh and S. Hara, Interior-point methods for the monotone semidefinite linear eomplementarity problem in symmetrie matrices. SIAM X Optim. 7 (1997) 86-125. | MR | Zbl

14. N. Megiddo, Pathways to the optimal set in linear programming, in Progress in Mathematical Programming-Interior Point and Related Methods, edited by N. Megiddo. Springer-Verlag, New York (1988) 131-158. | MR | Zbl

15. N. Megiddo and M. Schub, Boundary behavior of interior point algorithms in linear programming. Math. Oper. Res. 14 (1989) 97-146. | MR | Zbl

16. R. Monteiro and I. Adler, Interior path following primal-dual algorithms. Part I: Linear Programming. Math. Programming 44 (1989) 27-41. | MR | Zbl

17. R. Monteiro and T. Tsuchiya, Limiting behavior of the derivatives of certain trajectories associated with a monotone horizontal linear complementarity problem. Math. Oper. Res. 21 (1996) 129-148. | MR | Zbl

18. R. Monteiro and F. Zhou, On the existence and convergence of the central path for convex programming and some duality results, Comput Optim. Appl. 10 (1998) 51-77. | MR | Zbl

19. Y. Nesterov, Primal-dual methods. Seminar at CORE, Université Catholique de Louvain (1994).

20. M. L. Overton and R. S. Womersley, Second derivatives for optimization eigenvalues of symetric matrices. SIAM J. Matrix Anal. Appl 16 ( 1995697-718. | MR | Zbl

21. G. R. Parissot Résolution numérique approchée du problème de programation linéaire par application de la programation logarithmique. Revue Française Recherche Opérationelle 20 (1961) 227-259.

22. J. Renegar A Polynomial-Time Algorithm Based on Newton's Method for Linear Programming. Math. Programming 40 (1988) 59-94. | MR | Zbl

23. R. T. Rockafellar, Convex Analysis. Princeton University Press, New Jersey (1970). | MR | Zbl

24. A. Shapiro, First and second order analysis of nonlinear semidefinite programs. Math. Programming 77 (1997) 301-320. | MR | Zbl

25. A. Shapiro and M. K. H. Fan, On eigenvalue optimization. SIAM J. Optim. 5 (1995) 552-569. | MR | Zbl

26. G. Sonnevend, An analytic center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming. Springer-Verlag, New York, NY, Lecture Notes in Control and Inform. Sel 84 (1985) 866-876. | MR | Zbl

27. L. Vandenberghe and S. Boyd, Positive-Definite Programming, Mathematical Programming: State of the Art, edited by J. R. Birge, K. G. M. Murty, University of Michigan, Ann Arbor, MI (1994) 276-308. | Zbl