Convexity with respect to families of sections and lines and their application in optimization (Q280085)
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scientific article; zbMATH DE number 6575306
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convexity with respect to families of sections and lines and their application in optimization |
scientific article; zbMATH DE number 6575306 |
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Convexity with respect to families of sections and lines and their application in optimization (English)
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29 April 2016
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The author introduces the notions of \(\Gamma\)-convex and \(\Pi\)-convex functions. These generalized convexity notions are not completely independent from each other. Every \(\Pi\)-convex function is also \(\Gamma\)-convex, but the converse is false in general. He studies properties and characterizations of generalized convexity and applies for deriving first-order optimality conditions.
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generalized convexity
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generalized directional derivative
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characterization of generalized convexity
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optimality conditions
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