Optimization of convex functions on w*-compact sets (Q750817)
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scientific article; zbMATH DE number 4175727
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Optimization of convex functions on w*-compact sets |
scientific article; zbMATH DE number 4175727 |
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Optimization of convex functions on w*-compact sets (English)
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1990
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The authors give an iterative proof for the following result which is implicitly contained in the papers of Ghossoub and Maurey, respectively Lindenstrauss: Let \(\phi\) be a \(w^*\)-lower semicontinuous convex Lipschitz function defined on a \(w^*\)-compact convex set C in a dual Banach space \(X^*\). Given, \(\epsilon >0\), there is an \(x\in X\), with \(\| x\| \leq \epsilon\), such that \(\phi +x\) attains its supremum on C at an extreme point of C. Applications to the geometry of convex sets are given.
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optimization of convex functions
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perturbation by linear functionals
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\(w^ *\)-lower semicontinuous convex Lipschitz function defined on a \(w^ *\)-compact convex set
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dual Banach space
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geometry of convex sets
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