An infinitesimal local optimum of a set function (Q1271987)
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scientific article; zbMATH DE number 1225789
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An infinitesimal local optimum of a set function |
scientific article; zbMATH DE number 1225789 |
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An infinitesimal local optimum of a set function (English)
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22 November 1998
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The author considers the problem of finding an optimum of a function defined on some measure algebra. Using the language of nonstandard analysis, the author introduces the notion of an infinitesimal optimal solution. A nonstandard criterion of differentiability for set functions and necessary and sufficient conditions for the existence of an infinitesimal local optimum of differentiable set functions are obtained. This criterion is an infinitesimal version of a result of \textit{R. J. T. Morris} [J. Math. Anal. Appl. 70, 546-562 (1979; Zbl 0417.49032)].
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infinitesimal differentiability
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locally convex function
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infinitesimal local minimum
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infinitesimal separation
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nonstandard analysis
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0.7501381039619446
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0.748954176902771
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