The long-step method of analytic centers for fractional problems
Nemirovski, A. (Technion - Israel Institute of Technology)

Date:	1997
Abstract:	We develop a long-step surface-following version of the method of analytic centers for the fractional-linear problem min {t_0 t_0B(x) - A(x) (is in) H,B (x) (is in) K, x (is in) G}, where H is a closed convex domain, K is a convex cone contained in the recessive cone of H, G is a convex domain and B(·), A(·) are affine mappings. Tracing a two-dimensional surface of analytic centers rather than the usual path of centers allows to skip the initial "centering" phase of the path-following scheme. The proposed long-step policy of tracing the surface fits the best known overall polynomial-time complexity bounds for the method and, at the same time, seems to be more attractive computationally than the short-step policy, which was previously the only one giving good complexity bounds.
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Fractional programming ; Generalized eigenvalue problem ; Interior point methods ; Analytic centers
Published in:	Mathematical Programming, vol. 77 n. 2 (1997) p. 191-224, ISSN 0025-5610

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