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Notions of Relative Interior in Banach Spaces

Borwein, Jonathan M. and Goebel, Rafal (2003) Notions of Relative Interior in Banach Spaces. Journal of Mathematical Sciences , 115 . pp. 2542-2553.

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      Abstract

      Extensions to a Banach space of the equivalent notions of relatively absorbing, non-support, and relative interior points of a convex set in $\reals^n$ are presented. The relations between these extensions are studied, and their basic calculus rules are developed. Several explicit examples and counterexamples in general Banach spaces are given; and the tools for development of further examples are explained. Various implications for infinite dimensional optimization are highlighted.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: relative interior, constraint qualification, separation of convex sets, Fenchel duality, support point, absorbing point
      Subjects: 90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming
      46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices
      52-xx Convex and discrete geometry > 52Axx General convexity
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 24 Nov 2003
      Last Modified: 13 Jan 2015 11:49
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/138

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