Full Stability of General Parametric Variational Systems
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| Název: | Full Stability of General Parametric Variational Systems |
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| Autoři: | Tran T. A. Nghia, Boris S. Mordukhovich, D. T. Pham |
| Zdroj: | Set-Valued and Variational Analysis. 26:911-946 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Springer Science and Business Media LLC, 2018. |
| Rok vydání: | 2018 |
| Témata: | Prox-regularity, 49J53, 49J52, 90C31, 0211 other engineering and technologies, 02 engineering and technology, 01 natural sciences, Polyhedricity, Generalized differentiation, Optimization and Control (math.OC), Lipschitzian and Hölderian full stability, Variational inequalities and variational conditions, FOS: Mathematics, Legendre forms, Subgradients, Coderivatives, 0101 mathematics, Variational analysis, Parametric variational systems, Mathematics - Optimization and Control |
| Popis: | The paper introduces and studies the notions of Lipschitzian and H��lderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial subgradients of prox-regular functions acting in Hilbert spaces. Employing advanced tools and techniques of second-order variational analysis allows us to establish complete characterizations of, as well as directly verifiable sufficient conditions for, such full stability notions under mild assumptions. Furthermore, we derive exact formulas and effective quantitative estimates for the corresponding moduli. The obtained results are specified for important classes of variational inequalities and variational conditions in both finite and infinite dimensions. arXiv admin note: text overlap with arXiv:1409.2018 |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 1877-0541 1877-0533 |
| DOI: | 10.1007/s11228-018-0474-7 |
| DOI: | 10.48550/arxiv.1708.06631 |
| Přístupová URL adresa: | http://arxiv.org/pdf/1708.06631 http://arxiv.org/abs/1708.06631 https://link.springer.com/article/10.1007/s11228-018-0474-7 |
| Rights: | Springer TDM arXiv Non-Exclusive Distribution |
| Přístupové číslo: | edsair.doi.dedup.....73b7c5d645c5ef18e17c915c6a41b2bd |
| Databáze: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | The paper introduces and studies the notions of Lipschitzian and H��lderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial subgradients of prox-regular functions acting in Hilbert spaces. Employing advanced tools and techniques of second-order variational analysis allows us to establish complete characterizations of, as well as directly verifiable sufficient conditions for, such full stability notions under mild assumptions. Furthermore, we derive exact formulas and effective quantitative estimates for the corresponding moduli. The obtained results are specified for important classes of variational inequalities and variational conditions in both finite and infinite dimensions.<br />arXiv admin note: text overlap with arXiv:1409.2018 |
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| ISSN: | 18770541 18770533 |
| DOI: | 10.1007/s11228-018-0474-7 |