Minimum recession-compatible subsets of closed convex sets

نویسندگان

  • Yiran He
  • Jie Sun
چکیده

A subset B of a closed convex set A is recession-compatible with respect to A if A can be expressed as the Minkowski sum of B and the recession cone of A. We show that if A contains no line, then there exists a recession-compatible subset of A that is minimum with respect to set inclusion. The proof only uses basic facts of convex analysis and does not depend on Zorn’s Lemma. An application of this result to the error bound theory in optimization is presented.

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عنوان ژورنال:
  • J. Global Optimization

دوره 52  شماره 

صفحات  -

تاریخ انتشار 2012