@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://archive.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://archive.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://archive.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://archive.numdam.org/item/RO_2000__34_3_331_0/
1. Complementarity and nondegeneracy in semidefinite programming. Math. Programming 77 (1997) 111-128. | MR | Zbl
, and ,2. The non-linear geometry of linear programming. AT & Bell Laboratories, Murray Hill, NJ (1986), preprint. | Zbl
and ,3. Nonlinear Programming: Sequential Unconstrained Techniques. Classics in Applied Mathematics, SIAM Publications, Philadelphia (1990). | MR | Zbl
and ,4. Interior point trajectories in semidefinite programming (1996) preprint. | Zbl
and ,5. 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. Welldefinedness and limiting behavior of the central path. Computational and Applied Mathematics (accepted). | Zbl
and ,7. 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).
and8. On well definedness of the central path. J. Optim. Theory Appl. 102 (1999) 223-237. | MR | Zbl
and ,9. Central paths, generalized proximal point methods and Cauchy trajectories in Riemann manifolds. SIAM J. Control Optim. 37 (1999) 566-588. | MR | Zbl
, and ,10. A new polynomial time algorithm for linear programming, Combinatorica 4 (1984) 373-395. | MR | Zbl
,11. A polynomial algorithm for linear programming, Soviet Math. Dokl 20 (1979) 191-194. | Zbl
,11. Limiting behavior of trajectories by a continuation method for complementary problems. Math. Oper. Res. 15 (1990) 662-675. | MR | Zbl
, and ,13. Interior-point methods for the monotone semidefinite linear eomplementarity problem in symmetrie matrices. SIAM X Optim. 7 (1997) 86-125. | MR | Zbl
, and ,14. 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. Boundary behavior of interior point algorithms in linear programming. Math. Oper. Res. 14 (1989) 97-146. | MR | Zbl
and ,16. Interior path following primal-dual algorithms. Part I: Linear Programming. Math. Programming 44 (1989) 27-41. | MR | Zbl
and ,17. 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
and ,18. 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
and ,19. Primal-dual methods. Seminar at CORE, Université Catholique de Louvain (1994).
,20. Second derivatives for optimization eigenvalues of symetric matrices. SIAM J. Matrix Anal. Appl 16 ( 1995697-718. | MR | Zbl
and ,21. Résolution numérique approchée du problème de programation linéaire par application de la programation logarithmique. Revue Française Recherche Opérationelle 20 (1961) 227-259.
22. A Polynomial-Time Algorithm Based on Newton's Method for Linear Programming. Math. Programming 40 (1988) 59-94. | MR | Zbl
23. Convex Analysis. Princeton University Press, New Jersey (1970). | MR | Zbl
,24. First and second order analysis of nonlinear semidefinite programs. Math. Programming 77 (1997) 301-320. | MR | Zbl
,25. On eigenvalue optimization. SIAM J. Optim. 5 (1995) 552-569. | MR | Zbl
and ,26. 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. 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
and ,