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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.12895 |
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| _version_ | 1866929635316465664 |
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| author | Zhou, Li-wen Tang, Min Yi, Ya-ling Zhang, Yao-Jia |
| author_facet | Zhou, Li-wen Tang, Min Yi, Ya-ling Zhang, Yao-Jia |
| contents | This paper introduces and studies the generalized optimization problem (for short, GOP) defined by the conic order relation on a local sphere. The existence of solution to this problem is studied by using image space analysis (for short, ISA), and a class of regular weak separation functions on the local sphere is established. Moreover, a Lagrangian-type sufficient optimality condition and a saddle-point-type necessary optimality condition for GOP is obtained by a second class of weak separation functions, which are based on the Gerstewitz function and the directional distance function. The problem is transformed into a solvable real-valued optimization problem using scalarization methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12895 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Image Space Analysis to the generalized optimization problem on a local sphere Zhou, Li-wen Tang, Min Yi, Ya-ling Zhang, Yao-Jia Optimization and Control This paper introduces and studies the generalized optimization problem (for short, GOP) defined by the conic order relation on a local sphere. The existence of solution to this problem is studied by using image space analysis (for short, ISA), and a class of regular weak separation functions on the local sphere is established. Moreover, a Lagrangian-type sufficient optimality condition and a saddle-point-type necessary optimality condition for GOP is obtained by a second class of weak separation functions, which are based on the Gerstewitz function and the directional distance function. The problem is transformed into a solvable real-valued optimization problem using scalarization methods. |
| title | Image Space Analysis to the generalized optimization problem on a local sphere |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2412.12895 |