Generic stability of the solution mapping for set-valued optimization problems Article Swipe

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Xian-Jun Long , Yingquan Huang , Liping Tang ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.1186/s13660-015-0875-1

In this paper, we consider the generic stability of the weakly efficient solution mapping for set-valued optimization problems. Firstly, we obtain the upper semicontinuity of the weakly efficient solution mapping for set-valued optimization problems. Secondly, we show that, in the sense of Baire category, most set-valued optimization problems are stable. Finally, we give sufficient conditions ensuring the existence of essential. Our results extend and improve the corresponding results of Song et al. (J. Optim. Theory Appl. 156:591-599, 2013).

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Mathematics Set (abstract data type) Stability (learning theory) Optimization problem Solution set Baire category theorem Mathematical optimization Vector optimization Applied mathematics Discrete mathematics Computer science Multi-swarm optimization Machine learning Programming language

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Type: article
Language: en
Landing Page: https://doi.org/10.1186/s13660-015-0875-1
PDF: https://journalofinequalitiesandapplications.springeropen.com/track/pdf/10.1186/s13660-015-0875-1
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DOI: https://doi.org/10.1186/s13660-015-0875-1

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Title: Generic stability of the solution mapping for set-valued optimization problems

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Language: en

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Publication year: 2015

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Publication date: 2015-11-04

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Authors: Xian-Jun Long, Yingquan Huang, Liping Tang

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Landing page: https://doi.org/10.1186/s13660-015-0875-1

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Concepts: Mathematics, Set (abstract data type), Stability (learning theory), Optimization problem, Solution set, Baire category theorem, Mathematical optimization, Vector optimization, Applied mathematics, Discrete mathematics, Computer science, Multi-swarm optimization, Machine learning, Programming language

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