LOJASIEWCZ INEQUALITY FOR DEFINABLE FUNCTIONS IN THE O-MINIMAL STRUCTURES ON A REAL CLOSED FIELD

Authors

  • Trần Thống Nhất Post and Telecommunications Institute of Technology, Ho Chi Minh City, Viet Nam

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.

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Published

30-09-2014

Volume and Issues

Section

Natural Sciences and Technology

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)