Nonlinear Separation Theorems for Co-Radiant Sets and Optimality Conditions for Approximate and Proper Approximate Solutions in Vector Optimization
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908816503734272 |
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| author | García-Castaño, Fernando Melguizo-Padial, Miguel Ángel |
| author_facet | García-Castaño, Fernando Melguizo-Padial, Miguel Ángel |
| contents | This paper deals with $\varepsilon$-efficient and $\varepsilon$-properly efficient points with respect to a co-radiant set in vector optimization problems. In the first part of the paper, we establish a new nonlinear separation theorem for co-radiant sets in normed spaces. Subsequently, we obtain necessary and sufficient conditions, via scalarization, for both $\varepsilon$-efficient and $\varepsilon$-properly efficient points in a general framework, without requiring any assumptions on the co-radiant set or convexity conditions on the sets under consideration. Consequently, our results are applicable in a broader range of settings than those previously addressed in the literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_10193 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear Separation Theorems for Co-Radiant Sets and Optimality Conditions for Approximate and Proper Approximate Solutions in Vector Optimization García-Castaño, Fernando Melguizo-Padial, Miguel Ángel Optimization and Control 46N10, 90C26, 90C29, 49K27 This paper deals with $\varepsilon$-efficient and $\varepsilon$-properly efficient points with respect to a co-radiant set in vector optimization problems. In the first part of the paper, we establish a new nonlinear separation theorem for co-radiant sets in normed spaces. Subsequently, we obtain necessary and sufficient conditions, via scalarization, for both $\varepsilon$-efficient and $\varepsilon$-properly efficient points in a general framework, without requiring any assumptions on the co-radiant set or convexity conditions on the sets under consideration. Consequently, our results are applicable in a broader range of settings than those previously addressed in the literature. |
| title | Nonlinear Separation Theorems for Co-Radiant Sets and Optimality Conditions for Approximate and Proper Approximate Solutions in Vector Optimization |
| topic | Optimization and Control 46N10, 90C26, 90C29, 49K27 |
| url | https://arxiv.org/abs/2503.10193 |