Łojasiewicz-type inequalities and global error bounds for nonsmooth definable functions in o-minimal structures (Q2786583)
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scientific article; zbMATH DE number 6541567
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Łojasiewicz-type inequalities and global error bounds for nonsmooth definable functions in o-minimal structures |
scientific article; zbMATH DE number 6541567 |
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15 February 2016
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Łojasiewicz inequalities
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error bounds
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o-minimal structures
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nonsmooth analysis
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Łojasiewicz-type inequalities and global error bounds for nonsmooth definable functions in o-minimal structures (English)
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The author extends some results of \textit{H. H. Vui} [SIAM J. Optim. 23, No. 2, 917--933 (2013; Zbl 1273.32014)] from polynomial functions to continuous functions definable in an o-minimal structure. More precisely: Some Łojasiewicz-type inequalities for continuous definable functions are proved. A criterion for a global error bound for continuous definable functions is given. The relation of this error bound with the Palais-Smale condition is clarified. A Łojasiewicz nonsmooth gradient inequality at infinity near the fiber for continuous definable functions is given and characterized.
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