$\ell_0$-Norm Multiobjective Optimization Models Motivated by Applications to Proton Therapy
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912577737457664 |
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| author | Cong, Xiaoda Ding, Xuanfeng Mordukhovich, Boris Nguyen, Anh Vu Zhao, Lewei |
| author_facet | Cong, Xiaoda Ding, Xuanfeng Mordukhovich, Boris Nguyen, Anh Vu Zhao, Lewei |
| contents | The paper is devoted to investigating single-objective and multiobjective optimization problems involving the $\ell_0$-norm function, which is nonconvex and nondifferentiable. Our motivation comes from proton beam therapy models in cancer research. The developed approach uses subdifferential tools of variational analysis and the Gerstewitz (Tammer) scalarization function in multiobjective optimization. Based on this machinery, we propose several algorithms of the subgradient type and conduct their convergence analysis. The obtained results are illustrated by numerical examples, which reveal some characteristic features of the proposed algorithms and their interactions with the gradient descent. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_06833 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\ell_0$-Norm Multiobjective Optimization Models Motivated by Applications to Proton Therapy Cong, Xiaoda Ding, Xuanfeng Mordukhovich, Boris Nguyen, Anh Vu Zhao, Lewei Optimization and Control 90C26, 90C29, 49J52 The paper is devoted to investigating single-objective and multiobjective optimization problems involving the $\ell_0$-norm function, which is nonconvex and nondifferentiable. Our motivation comes from proton beam therapy models in cancer research. The developed approach uses subdifferential tools of variational analysis and the Gerstewitz (Tammer) scalarization function in multiobjective optimization. Based on this machinery, we propose several algorithms of the subgradient type and conduct their convergence analysis. The obtained results are illustrated by numerical examples, which reveal some characteristic features of the proposed algorithms and their interactions with the gradient descent. |
| title | $\ell_0$-Norm Multiobjective Optimization Models Motivated by Applications to Proton Therapy |
| topic | Optimization and Control 90C26, 90C29, 49J52 |
| url | https://arxiv.org/abs/2509.06833 |