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Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization

Bauschke, Heinz H. and Borwein, Jonathan M. and Li, Wu (1999) Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization. Mathematical Programming, 86 . pp. 135-160.

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      Abstract

      The strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. These fundamental notions occur in various branches of convex optimization (constrained approximation, convex feasibility problems, linear inequalities, for instance). It is shown that the standard constraint qualification from convex analysis implies bounded linear regularity, which in turn yields the strong conical hull intersection property. Jameson's duality for two cones, which relates bounded linear regularity to property~(G), is re-derived and refined. For polyhedral cones, a statement dual to Hoffman's error bound result is obtained. A sharpening of a result on error bounds for convex inequalities by Auslender and Crouzeix is presented. Finally, for two subspaces, property~(G) is quantified by the angle between the subspaces.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: angle, asymptotic constraint qualification, basic constraint qualification, bounded linear regularity, CHIP, conical hull intersection property, convex feasibility problem, convex inequalities, constrained best approximation, error bound, Friedrichs angle, Hoffman's error bound, linear inequalities, linear regularity, orthogonal projection, property (G)
      Subjects: 90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming
      46-xx Functional analysis > 46Axx Topological linear spaces and related structures
      15-xx Linear and multilinear algebra; matrix theory
      41-xx Approximations and expansions > 41Axx Approximations and expansions
      46-xx Functional analysis > 46Cxx Inner product spaces and their generalizations, Hilbert spaces
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 25 Nov 2003
      Last Modified: 13 Jan 2015 13:27
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/195

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