Minimum recession-compatible subsets of closed convex sets
نویسندگان
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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ورودعنوان ژورنال:
- J. Global Optimization
دوره 52 شماره
صفحات -
تاریخ انتشار 2012