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Abstract: For a conic optimization problem P : minimize x c T x s.t. Ax = b x 2 C and its dual: D : supremum y;s b T y s.t. A T y + s = c s 2 C ; we present a geometric relationship between the maximum norms of the level sets of the primal and the inscribed sizes of the level sets of the dual (or the other way around). AMS Subject Classi cation: 90C, 90C05, 90C60 Keywords: Convex Optimization, Conic Optimization, Duality, Level Sets 1 This research has been partially supported through... (Update)
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.... also see the measure g( proposed by Freund [11] and a related geometric approach to primal dual level sets in convex optimization [12]) We also consider the condition measure of Renegar (see [27, 26] In the context of strong infeasibility certi cates, we generalize a...
.... # optimal solution set (which would be infinite in this case) rather than the minimum distance (which would be finite in this case) Also, in [1] in the case of conic optimization with x = 0, it is shown that D # defined using (7) is inversely proportional to the size of the...
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2: Some Perturbation Theory for Linear Programming - Renegar - 1994
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BibTeX entry: (Update)
R. M. Freund, On the primal-dual geometry of level sets in linear and conic optimization, July 2001. http://citeseer.ist.psu.edu/freund01primaldual.html More
@techreport{ freund01primaldual,
author = "R. M. Freund",
title = "On the Primal-Dual Geometry of Level Sets in Linear and Conic Optimization",
address = "Cambridge, MA",
year = "2001",
url = "citeseer.ist.psu.edu/freund01primaldual.html" }
Citations (may not include all citations):326 Interior-Point Polynomial Algorithms in Convex Programming (context) - Nesterov, Nemirovskii - 1994
17 Condition-based complexity of convex optimization in conic l.. - Freund, Vera - 1999
16 Some characterizations and properties of the \distance to il.. - Freund, Vera - 1999
7 Duality and asymptotic solvability over cones (context) - Ben-Israel, Charnes et al. - 1969
1 Innite programs (context) - Dun - 1956
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