Global holderian error bounds for differential semi-algebraic functions

Authors

  • Phi-Dung Hoang Department of Mathematics, Faculty of Fundamental Sciences, Posts and Telecommunications Institute of Technology, Ha noi, Vietnam

DOI:

https://doi.org/10.56764/hpu2.jos.2022.1.1.10-15

Abstract

In this paper, we extend some results in [5] of H. V. Hà and P. D. Hoàng on global Holderian error bounds of the sub-level set:

from polynomial functions to semi-algebraic functions. Moreover, we give some examples which show the difference between polynomial functions and semi-algebraic functions

References

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J. Bochnak, M. Coste and M.-F. Roy, Real Algebraic Geometry, Springer, 1998.

S. T. Dinh, H. V. Hà and T. S. Phạm, Holder-Type Global Error Bounds for Non-degenerate Polynomial Systems, Acta Mathematica Vietnamica, 42 (2017), 563–585.

H. V. Hà, Global Holderian error bound for non-degenerate polynomials, SIAM. J. Optim., 23 (2013), No. 2, 917-933.

H. V. Hà, P. D. Hoàng, Fedoryuk values and stability of global Holderian error bounds for polynomial functions, Arxiv: 1902.05972, 2019.

H. V. Hà, T. S. Phạm, Genericity in polynomial optimization, World Scientific Publishing, 2017.

P. D. Hoàng, Lojasiewicz-type inequalities and global error bounds for nonsmooth definable functions in o-minimal structures, Bull. Aust. Math. Soc. 93 (2016), 99-112.

K. Kurdyka, P. Orro, S. Simon, Semialgebraic Sard theorem for generalized critical values, J. Diff. Geom. 56 (2000), 67-92.

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Published

31-08-2022

How to Cite

Hoang, P.-D. (2022). Global holderian error bounds for differential semi-algebraic functions. HPU2 Journal of Science: Natural Sciences and Technology, 1(1), 10–15. https://doi.org/10.56764/hpu2.jos.2022.1.1.10-15

Volume and Issue

Section

Natural Sciences and Technology