Characterizations of evenly convex sets and evenly quasiconvex functions
An evenly convex set \(K\) in a Banach space is the intersection of open half spaces. It is shown that this is equivalent to saying that for any closure point \(x\) of \(K\) not in \(K\), no translate through \(x\), of any linear subspace of the tangent cone at \(x\), meets \(K\). This yields a fully primal characterization of evenly quasiconvex functions on a separable Banach space (having evenly convex lower level sets), i.e. not referring to dual functionals and/or separation properties.
scientific article; zbMATH DE number 1866597
scientific article