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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/2409.13635 |
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| _version_ | 1866912037976670208 |
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| author | Long, Vo Si Trong Nam, Nguyen Mau Tran, Tuyen Van, Nguyen Thi Thu |
| author_facet | Long, Vo Si Trong Nam, Nguyen Mau Tran, Tuyen Van, Nguyen Thi Thu |
| contents | This paper has two primary objectives. First, we investigate fundamental qualitative properties of the generalized multi-source Weber problem formulated using the Minkowski gauge function. This includes proving the existence of global optimal solutions, demonstrating the compactness of the solution set, and establishing optimality conditions for these solutions. Second, we apply Nesterov's smoothing and the adaptive Boosted Difference of Convex functions Algorithm (BDCA) to solve both the unconstrained and constrained versions of the generalized multi-source Weber problems. These algorithms build upon the work presented in [6,19]. We conduct a comprehensive evaluation of the adaptive BDCA, comparing its performance to the method proposed in [19], and provide insights into its efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13635 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Qualitative Analysis and Adaptive Boosted DCA for Generalized Multi-Source Weber Problems Long, Vo Si Trong Nam, Nguyen Mau Tran, Tuyen Van, Nguyen Thi Thu Optimization and Control This paper has two primary objectives. First, we investigate fundamental qualitative properties of the generalized multi-source Weber problem formulated using the Minkowski gauge function. This includes proving the existence of global optimal solutions, demonstrating the compactness of the solution set, and establishing optimality conditions for these solutions. Second, we apply Nesterov's smoothing and the adaptive Boosted Difference of Convex functions Algorithm (BDCA) to solve both the unconstrained and constrained versions of the generalized multi-source Weber problems. These algorithms build upon the work presented in [6,19]. We conduct a comprehensive evaluation of the adaptive BDCA, comparing its performance to the method proposed in [19], and provide insights into its efficiency. |
| title | Qualitative Analysis and Adaptive Boosted DCA for Generalized Multi-Source Weber Problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2409.13635 |