Robust Optimization Approach for Solving Uncertain Multiobjective Optimization Problems Using the Projected Gradient Method
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915188312113152 |
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| author | Kumar, Shubham Mahatoa, Nihar Kumar Ghosh, Debdas |
| author_facet | Kumar, Shubham Mahatoa, Nihar Kumar Ghosh, Debdas |
| contents | Numerous real-world applications of uncertain multiobjective optimization problems (UMOPs) can be found in science, engineering, business, and management. To handle the solution of uncertain optimization problems, robust optimization is a relatively new field. An extended version of the projected gradient method (PGM) for a deterministic smooth multiobjective optimization problem (MOP) is presented in the current study as a PGM for UMOP. An objective-wise worst-case cost (OWWC) type robust counterpart is considered, and the PGM is used to solve a UMOP by using OWWC. A projected gradient descent algorithm is created using theoretical findings. It is demonstrated that the projected gradient descent algorithm's generated sequence converges to the robust counterpart's weak Pareto optimal solution, which will be the robust weak Pareto optimal solution for UMOP. Under a few reasonable presumptions, the projected gradient descent algorithm's full convergent behavior is also justified. Finally, numerical tests are presented to validate the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Optimization Approach for Solving Uncertain Multiobjective Optimization Problems Using the Projected Gradient Method Kumar, Shubham Mahatoa, Nihar Kumar Ghosh, Debdas Optimization and Control Numerous real-world applications of uncertain multiobjective optimization problems (UMOPs) can be found in science, engineering, business, and management. To handle the solution of uncertain optimization problems, robust optimization is a relatively new field. An extended version of the projected gradient method (PGM) for a deterministic smooth multiobjective optimization problem (MOP) is presented in the current study as a PGM for UMOP. An objective-wise worst-case cost (OWWC) type robust counterpart is considered, and the PGM is used to solve a UMOP by using OWWC. A projected gradient descent algorithm is created using theoretical findings. It is demonstrated that the projected gradient descent algorithm's generated sequence converges to the robust counterpart's weak Pareto optimal solution, which will be the robust weak Pareto optimal solution for UMOP. Under a few reasonable presumptions, the projected gradient descent algorithm's full convergent behavior is also justified. Finally, numerical tests are presented to validate the proposed method. |
| title | Robust Optimization Approach for Solving Uncertain Multiobjective Optimization Problems Using the Projected Gradient Method |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.06509 |