Abstract
The Frank—Wolfe theorem states that a quadratic function, bounded below on a nonempty polyhedral convex set, attains its infimum there. This paper gives sufficient conditions under which a function either attains its infimum on a nonempty polyhedral convex set or is unbounded below on some halfline of that set. Quadratic functions are shown to satisfy these sufficient conditions.
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Research and reproduction of this report were partially supported by the National Science Foundation Grant MCS76-81259; and the Office of Naval Research Contract N00014-75-C-0267.
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Perold, A.F. A generalization of the Frank—Wolfe theorem. Mathematical Programming 18, 215–227 (1980). https://doi.org/10.1007/BF01588315
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DOI: https://doi.org/10.1007/BF01588315