Primal-dual interior-point methods for self-scaled cones
(1998) SIAM Journal on Optimization — Vol. 8, n° 2, p. 324-364 (1998)
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- Abstract
- In this paper we continue the development of a theoretical foundation for efficient primal-dual interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled (see Yu. E. Nesterov and M.J. Todd, Math. Oper. Res., 22 (1997), pp. 1-42). The class of problems under consideration includes linear programming, semidefinite programming, and convex quadratically constrained, quadratic programming problems. For such problems we introduce a new definition of affine-scaling and centering directions. We present efficiency estimates for several symmetric primal-dual methods that can loosely be classified as path-following methods. Because of the special properties of these cones and barriers, two of our algorithms can take steps that typically go 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. (1998). Primal-dual interior-point methods for self-scaled cones. SIAM Journal on Optimization, 8(2), 324-364. https://doi.org/10.1137/S1052623495290209 (Original work published 1998)