Self-scaled cones and interior-point methods in nonlinear programming (1994) [24 citations — 1 self]
by Yu. E. Nesterov, M. J. Todd
Working Paper, CORE, Catholic University of Louvain, Louvain-la-Neuve
http://karush.rutgers.edu/~alizadeh/Sdppage/Todd/nesto15.ps
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@INPROCEEDINGS{Nesterov94self-scaledcones,author = {Yu. E. Nesterov and M. J. Todd},
title = {Self-scaled cones and interior-point methods in nonlinear programming},
booktitle = {Working Paper, CORE, Catholic University of Louvain, Louvain-la-Neuve},
year = {1994}
}
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Abstract:
Abstract: This paper provides a theoretical foundation for efficient interior-point algorithms for nonlinear programming problems expressed in conic form, when the cone and its associated barrier are self-scaled. For such problems we devise long-step and symmetric primal-dual methods. Because of the special properties of these cones and barriers, our algorithms can take steps that go typically a large fraction of the way to the boundary of the feasible region, rather than being confined to a ball of unit radius in the local norm defined by the Hessian of the barrier.
Citations
| 457 | A new polynomial-time algorithm for linear programming – Karmarkar - 1984 |
| 165 | Convex analysis and variational problems – Ekeland, Temam - 1976 |
| 53 | An O(pnL) iteration potential reduction algorithm for linear complementarity problems – Kojima, Mizuno, et al. - 1991 |
| 50 | A short-cut potential reduction algorithm for linear programming – Kaliski, Ye - 1993 |
| 30 | A centered projective algorithm for linear programming – Todd, Ye - 1990 |
| 25 | A polynomial method of approximate centers for linear programming – Roos, Vial - 1992 |
| 16 | Polynomial Affine Algorithms for Linear Programming – Gonzaga - 1990 |
| 15 | Long-step strategies in interior-point primal-dual methods – Nesterov - 1993 |
| 11 | Potential reduction polynomial time method for truss topology design – Ben-Tal, Nemirovskii - 1994 |
| 1 | A strengthened acceptance criterion for approximate projections in Karmarkar's algorithm – Anstreicher - 1986 |
