Abstract
In this paper, in contrast to the literature on the tilt-stability only dealing with local minima, we introduce and study the \(\psi \)-tilt-stable global minimum and stable global \(\varphi \)-well-posedness with \(\psi \) and \(\varphi \) being the so-called admissible functions. We adopt global strong metric regularity of the subdifferential mapping \({{\hat{\partial }}} f\) of the objective function f with respect to an admissible function \(\psi \) and prove that the global strong metric regularity of \(\hat{\partial }f\) at 0 with respect to \(\psi \) implies the stable global \(\varphi \)-well-posedness of f with \(\varphi (t)=\int _0^t\psi (s)ds\) and that if f is convex then the converse implication also holds. Moreover, we establish the relationships between \(\psi \)-tilt-stable global minimum and stable global \(\varphi \)-well-posedness. Our results are new even in the convexity case.
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This research was supported by the National Natural Science Foundation of People’s Republic of China (Grant Nos. 11771384 and 11801497), the Project for Innovation Team of Yunnan Province (202005AE160006) and the Project for Young-notch Talents in the Ten Thousand Talent Program of Yunnan Province.
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Zheng, X.Y., Zhu, J. Stable global well-posedness and global strong metric regularity. J Glob Optim 83, 359–376 (2022). https://doi.org/10.1007/s10898-021-01100-4
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DOI: https://doi.org/10.1007/s10898-021-01100-4