On the central path for nonlinear semidefinite programming
RAIRO - Operations Research - Recherche Opérationnelle, Tome 34 (2000) no. 3, pp. 331-345.

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     title = {On the central path for nonlinear semidefinite programming},
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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://geodesic.mathdoc.fr/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. | Zbl | MR

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). | Zbl | MR

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. | Zbl | MR

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. | Zbl | MR

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

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. | Zbl | MR

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. | Zbl | MR

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. | Zbl | MR

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

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

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. | Zbl | MR

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. | Zbl | MR

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. | Zbl | MR

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. | Zbl | MR

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

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

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

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. | Zbl | MR

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