Newton Method for Multiobjective Optimization Problems of Interval-Valued Maps
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918375466205184 |
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| author | Mondal, Tapas Ghosh, Debdas Kim, Do Sang |
| author_facet | Mondal, Tapas Ghosh, Debdas Kim, Do Sang |
| contents | In this article, we propose a Newton-based method for solving multiobjective interval optimization problems (MIOPs). We first provide a connection between weakly Pareto optimal points and Pareto critical points in the context of MIOPs. Introducing this relationship, we develop an algorithm aimed at computing a Pareto critical point. The algorithm incorporates the computation of a descent direction at a non-Pareto critical point and employs an Armijo-like line search strategy to ensure sufficient decrease. Under suitable assumptions, we prove that the sequence generated by our proposed algorithm converges to a Pareto critical point. The effectiveness and performance of the proposed method are demonstrated through a series of numerical experiments on some test problems. Finally, we apply our proposed algorithm in a portfolio optimization problem with interval uncertainty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06000 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Newton Method for Multiobjective Optimization Problems of Interval-Valued Maps Mondal, Tapas Ghosh, Debdas Kim, Do Sang Optimization and Control In this article, we propose a Newton-based method for solving multiobjective interval optimization problems (MIOPs). We first provide a connection between weakly Pareto optimal points and Pareto critical points in the context of MIOPs. Introducing this relationship, we develop an algorithm aimed at computing a Pareto critical point. The algorithm incorporates the computation of a descent direction at a non-Pareto critical point and employs an Armijo-like line search strategy to ensure sufficient decrease. Under suitable assumptions, we prove that the sequence generated by our proposed algorithm converges to a Pareto critical point. The effectiveness and performance of the proposed method are demonstrated through a series of numerical experiments on some test problems. Finally, we apply our proposed algorithm in a portfolio optimization problem with interval uncertainty. |
| title | Newton Method for Multiobjective Optimization Problems of Interval-Valued Maps |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.06000 |