Self-scaled barriers and interior-point methods for convex programming
(1997) Mathematics of operations research — Vol. 22, n° 1, p. 1-42 (1997)
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- Abstract
- This paper provides a theoretical foundation for efficient interior-point algorithms for convex 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.
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Nesterov, Y., & Todd, M. J. (1997). Self-scaled barriers and interior-point methods for convex programming. Mathematics of operations research, 22(1), 1-42. https://doi.org/10.1287/moor.22.1.1 (Original work published 1997)