Abstract
A local minimum of a quasiconvex function is not necessarily a global minimum. In this paper, we show that every lower semicontinuous quasiconvex function can be approximated uniformly by a sequence of quasiconvex functions for which every local minimum is a global minimum. We also study the continuity of the functions appearing in a recently obtained decomposition of quasiconvex functions.
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Acknowledgements
The authors are grateful to KFUPM, Dhahran, Saudi Arabia for providing excellent research facilities. They would also like to thank the referee for his/her useful comments and suggestions that helped to improve the paper.
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Dedicated to Nicolas Hadjisavvas on the occasion of his 65th birthday.
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Al-Homidan, S., Shaalan, L. Approximation of quasiconvex functions by neatly quasiconvex functions. Optim Lett 15, 979–989 (2021). https://doi.org/10.1007/s11590-020-01535-w
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DOI: https://doi.org/10.1007/s11590-020-01535-w