Stable global well-posedness and global strong metric regularity

Autor: Xi Yin Zheng, Jiangxing Zhu
Rok vydání: 2021
Předmět:
Zdroj: Journal of Global Optimization. 83:359-376
ISSN: 1573-2916
0925-5001
DOI: 10.1007/s10898-021-01100-4
Popis: 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.
Databáze: OpenAIRE
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