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A systematization of global well-posedness in vector optimization.

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Title: A systematization of global well-posedness in vector optimization.
Authors: Rocca, Matteo1 (AUTHOR) matteo.rocca@uninsubria.it
Source: Annals of Operations Research. Mar2025, Vol. 346 Issue 2, p1653-1669. 17p.
Subjects: Multi-objective optimization, Vector valued functions
Abstract: In this paper we give a systematization of global well-posedness in vector optimization. We investigate the links among global notions of well-posedness for a vector optimization problem (see e.g. Miglierina et al. in J Optim Theory Appl 126:391–409, 2005 for a detailed explanation of the difference between pointwise and global well-posedness in vector optimization). In particular we compare several notions of global well-posedness referring to efficient solutions, weakly efficient solutions and properly efficient solutions of a vector optimization problem. We also establish scalar characterizations of global vector well-posedness. Finally we study global well-posedness of vector cone-convex functions. [ABSTRACT FROM AUTHOR]
Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A systematization of global well-posedness in vector optimization.
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  Data: In this paper we give a systematization of global well-posedness in vector optimization. We investigate the links among global notions of well-posedness for a vector optimization problem (see e.g. Miglierina et al. in J Optim Theory Appl 126:391–409, 2005 for a detailed explanation of the difference between pointwise and global well-posedness in vector optimization). In particular we compare several notions of global well-posedness referring to efficient solutions, weakly efficient solutions and properly efficient solutions of a vector optimization problem. We also establish scalar characterizations of global vector well-posedness. Finally we study global well-posedness of vector cone-convex functions. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10479-024-06089-z
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        Text: English
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              Text: Mar2025
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