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- W3190911146 abstract "It is well known that a strictly convex minimand admits at most one minimizer. We prove a partial converse: Let $X$ be a locally convex Hausdorff space and $f colon X mapsto left( - infty , infty right]$ a function with compact sublevel sets and exhibiting some mildly superlinear growth. Then each tilted minimization problem begin{equation} label{eq. minimization problem} min_{x in X} f(x) - langle x' , x rangle_X end{equation} admits at most one minimizer as $x'$ ranges over $text{dom} left( partial f^* right)$ if and only if the biconjugate $f^{**}$ is essentially strictly convex and agrees with $f$ at all points where $f^{**}$ is subdifferentiable. We prove this via a representation formula for $f^{**}$ that might be of independent interest." @default.
- W3190911146 created "2021-08-16" @default.
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- W3190911146 date "2021-08-12" @default.
- W3190911146 modified "2023-09-27" @default.
- W3190911146 title "Unique Minimizers and the Representation of Convex Envelopes in Locally Convex Vector Spaces" @default.
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