A Trust Region Proximal Gradient Method for Nonlinear Multi-objective Optimization Problems
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929558262906880 |
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| author | Ansary, Md Abu Talhamainuddin |
| author_facet | Ansary, Md Abu Talhamainuddin |
| contents | In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth function. The proposed method is free from any kind of priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a sub problem is solved to find a suitable direction. This sub problem uses a quadratic approximation of each smooth function and a trust region constraint. An update formula for trust region radius is introduce in this paper. A sequence is generated using descent directions. It is justified that under some mild assumptions every accumulation point of this sequence is a critical point. The proposed method is verified and compared with some existing methods using a set of problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Trust Region Proximal Gradient Method for Nonlinear Multi-objective Optimization Problems Ansary, Md Abu Talhamainuddin Optimization and Control Numerical Analysis 90C25, 90C29, 49M37, 65K10 In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth function. The proposed method is free from any kind of priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a sub problem is solved to find a suitable direction. This sub problem uses a quadratic approximation of each smooth function and a trust region constraint. An update formula for trust region radius is introduce in this paper. A sequence is generated using descent directions. It is justified that under some mild assumptions every accumulation point of this sequence is a critical point. The proposed method is verified and compared with some existing methods using a set of problems. |
| title | A Trust Region Proximal Gradient Method for Nonlinear Multi-objective Optimization Problems |
| topic | Optimization and Control Numerical Analysis 90C25, 90C29, 49M37, 65K10 |
| url | https://arxiv.org/abs/2410.19502 |