Set intersection theorems and existence of optimal solutions (Q879966)
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scientific article; zbMATH DE number 5151338
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Set intersection theorems and existence of optimal solutions |
scientific article; zbMATH DE number 5151338 |
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Set intersection theorems and existence of optimal solutions (English)
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10 May 2007
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In this interesting paper one establishes sufficient conditions for a decreasing sequence of closed subsets of \(\mathbb{R}^{n}\) to have nonempty intersection. The conditions are formulated in terms of asymptotic directions, retractive directions and horizon directions. In order to apply the results to the existence of global solutions for constrained minimization problems one introduces the notion of bidirectionally flat convex functions. One recovers so the Frank-Wolfe theorem.
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set intersection
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asymptotic direction
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recession direction
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global minimum
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Frank-Wolfe theorem
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quasiconvex function
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