Sublinear Scalarizations for Proper and Approximate Proper Efficient Points in Nonconvex Vector Optimization
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | García-Castaño, Fernando Melguizo-Padial, Miguel Ángel Parzanese, G. |
| author_facet | García-Castaño, Fernando Melguizo-Padial, Miguel Ángel Parzanese, G. |
| contents | We show that under a separation property, a $\mathcal{Q}$-minimal point in a normed space is the minimum of a given sublinear function. This fact provides sufficient conditions, via scalarization, for nine types of proper efficient points; establishing a characterization in the particular case of Benson proper efficient points. We also obtain necessary and sufficient conditions in terms of scalarization for approximate Benson and Henig proper efficient points. The separation property we handle is a variation of another known property and our scalarization results do not require convexity or boundedness assumptions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_07352 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sublinear Scalarizations for Proper and Approximate Proper Efficient Points in Nonconvex Vector Optimization García-Castaño, Fernando Melguizo-Padial, Miguel Ángel Parzanese, G. Optimization and Control 90C26, 90C29, 90C30, 90C46, 49K27, 46N10 We show that under a separation property, a $\mathcal{Q}$-minimal point in a normed space is the minimum of a given sublinear function. This fact provides sufficient conditions, via scalarization, for nine types of proper efficient points; establishing a characterization in the particular case of Benson proper efficient points. We also obtain necessary and sufficient conditions in terms of scalarization for approximate Benson and Henig proper efficient points. The separation property we handle is a variation of another known property and our scalarization results do not require convexity or boundedness assumptions. |
| title | Sublinear Scalarizations for Proper and Approximate Proper Efficient Points in Nonconvex Vector Optimization |
| topic | Optimization and Control 90C26, 90C29, 90C30, 90C46, 49K27, 46N10 |
| url | https://arxiv.org/abs/2401.07352 |