Abstract
The scalar finite-dimensional case has been discussed in the first part of this work series, which aims at exploiting the image space analysis to establish a general regularity condition for constrained extremum problems. Based on this preliminary result, the present paper dedicates itself to further study the regularity conditions for vector constrained extremum problems in a Euclidean space. The case of infinite-dimensional image will be the subject of a subsequent paper.
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Acknowledgements
The authors are grateful for the kind hospitality of the institution when this work was carried out during a stay of the second author in the Department of Mathematics, University of Pisa. The authors express their gratitude to the anonymous referee for his/her valuable comments and suggestions, which help to improve the paper. This research was supported by China Scholarship Council, the National Natural Science Foundation of China (Grant: 11601437, 11526165) and the Fundamental Research Funds for the Central Universities (Grant: JBK1802067).
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Pellegrini, L., Zhu, S. Constrained Extremum Problems, Regularity Conditions and Image Space Analysis. Part II: The Vector Finite-Dimensional Case. J Optim Theory Appl 177, 788–810 (2018). https://doi.org/10.1007/s10957-018-1322-5
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DOI: https://doi.org/10.1007/s10957-018-1322-5
Keywords
- Image space analysis
- Vector optimization
- Regularity condition
- Constraint qualification
- Separation function