On the Riemannian Geometry Defined by Self-Concordant Barriers and Interior-Point Methods

Foundations of Computational Mathematics

Volumn 2, Issue 4, 2002, Pages 333-361

  Nesterov, Yu E ^a   Todd, M J ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b School of Operations Research and Industrial Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CENTRAL PATH; GEODESIC CURVES; INTERIOR-POINT METHOD; LINEAR FUNCTIONS; PRIMAL-DUAL; PROVIDE GUIDANCES; RIEMANNIAN GEOMETRY; SELF-CONCORDANT BARRIERS;

OPTIMIZATION; SET THEORY;

GEOMETRY;

EID: 0036435303     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s102080010032     Document Type: Article

References (14)

1. A. Edelman, T. Arias, and S. T. Smith, The geometry of algorithms with orthogonality constraints, SIAM J. on Matrix Anal. and Appl. 20 (1998), 303-353.
2. O. Güler, Barrier functions in interior-point methods, Math. of Oper. Res. 21 (1996), 860-885.
3. S. Helgason, Differential Geometry and Symmetric Spaces, American Mathematical Society, Providence, RI, 2000.
4. N. K. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984), 373-395.
5. N. K. Karmarkar, Riemannian geometry underlying interior-point methods for linear programming, in Mathematical Developments Arising from Linear Programming (J. C. Lagarias and M. J. Todd, eds.), Contemporary Mathematics, Vol. 114, American Mathematical Society, Providence, RI, 1990, pp. 51-75.
6. n, Amer. J. of Math. 79 (1957), 575-596.
7. Yu. E. Nesterov, Long-step strategies in interior-point primal-dual methods, Math. Programming 76 (1996), 47-94.
8. Yu. E. Nesterov and A. S. Nemirovskii, Interior Point Polynomial Methods in Convex Programming: Theory and Algorithms, SIAM, Philadelphia, PA, 1994.
9. Yu. E. Nesterov, M. J. Todd, and Y. Ye, Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems, Math. Programming 84 (1999), 227-267.
10. O. Rothaus, Domains of positivity, Abh. Math. Sem. Univ. Hamburg 24 (1960), 189-235.
11. K. Tanabe, Geometric method in nonlinear programming, J. of Optim. Theory Appl. 30 (1980), 181-210.
12. M. J. Todd, On adjusting parameters in homotopy methods for linear programming, in Approximation Theory and Optimization (M. Buhmann and A. Iserles, eds.), Cambridge University Press, Cambridge, 1997, pp. 201-220.
13. M. H. Wright, Interior methods for constrained optimization, in Acta Numerica 1992 (A. Iserles, ed.), Cambridge University Press, New York, 1992, pp. 341-407.
14. S. J. Wright, Primal-Dual Interior-Point Methods, SIAM, Philadelphia, PA, 1997.