A Set-Valued Lagrange Theorem based on a Process for Convex Vector Programming
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910301174104064 |
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| author | García-Castaño, Fernando Padial, M. A. Melguizo |
| author_facet | García-Castaño, Fernando Padial, M. A. Melguizo |
| contents | In this paper, we present a new set-valued Lagrange multiplier theorem for constrained convex set-valued optimization problems. We introduce the novel concept of Lagrange process. This concept is a natural extension of the classical concept of Lagrange multiplier where the conventional notion of linear continuous operator is replaced by the concept of closed convex process, its set-valued analogue. The behaviour of this new Lagrange multiplier based on a process is shown to be particularly appropriate for some types of proper minimal points and, in general, when it has a bounded base. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_10161 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Set-Valued Lagrange Theorem based on a Process for Convex Vector Programming García-Castaño, Fernando Padial, M. A. Melguizo Optimization and Control 90C29, 90C25, 90C31, 90C48 In this paper, we present a new set-valued Lagrange multiplier theorem for constrained convex set-valued optimization problems. We introduce the novel concept of Lagrange process. This concept is a natural extension of the classical concept of Lagrange multiplier where the conventional notion of linear continuous operator is replaced by the concept of closed convex process, its set-valued analogue. The behaviour of this new Lagrange multiplier based on a process is shown to be particularly appropriate for some types of proper minimal points and, in general, when it has a bounded base. |
| title | A Set-Valued Lagrange Theorem based on a Process for Convex Vector Programming |
| topic | Optimization and Control 90C29, 90C25, 90C31, 90C48 |
| url | https://arxiv.org/abs/2401.10161 |