Abstract
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 minimal 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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This research is partially supported by National Natural Science Foundation of China under Grant-10701059, and the PROVOST’S CHAIR Grant and the STAR Grant from School of Business, National University of Singapore.
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He, Y., Sun, J. Minimum recession-compatible subsets of closed convex sets. J Glob Optim 52, 253–263 (2012). https://doi.org/10.1007/s10898-011-9662-9
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DOI: https://doi.org/10.1007/s10898-011-9662-9