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About: Closed convex function     Goto   Sponge   NotDistinct   Permalink

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In mathematics, a function is said to be closed if for each , the sublevel setis a closed set. Equivalently, if the epigraph defined byis closed, then the function is closed. This definition is valid for any function, but most used for convex functions. A proper convex function is closed if and only if it is lower semi-continuous. For a convex function which is not proper there is disagreement as to the definition of the closure of the function.