LOJASIEWCZ INEQUALITY FOR DEFINABLE FUNCTIONS IN THE O-MINIMAL STRUCTURES ON A REAL CLOSED FIELD
DOI:
https://doi.org/10.37569/DalatUniversity.4.3&4.311(2014)Keywords:
Lojasiewicz inequality, O-minimal structures, Kurdyka-Lojasiewicz inequality.Abstract
Base on some results in [Bolte, A. Daniilidis, A. Lewis and M. Shiota, Clarke Subgra-dients of Stratifiable Functions, SIAM J. Optim, Vol. 18, No. 2, (2007), 556-572.], this article presents some results on Lojasiewicz inequality for definable functions in the o-minimal structures on a real closed field. Namely, we obtain the theorem on Kurdyka-Lojasiewicz inequality for a definable differentiable function and the nonsmooth extension of the above theorem.Downloads
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Published
30-09-2014
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Natural Sciences and Technology
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Copyright (c) 2014 Trần Thống Nhất

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
How to Cite
Nhất, T. T. (2014). LOJASIEWCZ INEQUALITY FOR DEFINABLE FUNCTIONS IN THE O-MINIMAL STRUCTURES ON A REAL CLOSED FIELD. Dalat University Journal of Science, 4(3&4), 5-19. https://doi.org/10.37569/DalatUniversity.4.3&4.311(2014)