Global Descent Method for Non-convex Multi-objective Optimization Problems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915417568575488 |
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| author | Adhikary, Bikram Ansary, Md Abu Talhamainuddin Treanta, Savin |
| author_facet | Adhikary, Bikram Ansary, Md Abu Talhamainuddin Treanta, Savin |
| contents | In this paper, we develop a global descent method for non-convex multi-objective optimization problems. The proposed approach builds upon foundational concepts from single-objective global descent techniques while removing the need for predefined scalars or ordering information of objective functions. Initially, the proposed method identifies a local weak efficient solution using any suitable descent algorithm, then applies an auxiliary function termed the multi-objective global descent function to systematically transition toward improved local weak efficient solutions. It is justified that this method can generate a global Pareto front for non-convex problems, which has many different local Pareto fronts. Finally, comprehensive numerical experiments on benchmark non-convex multi-objective optimization problems have been done to demonstrate the method's robustness, scalability and effectiveness of the proposed method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_22390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Descent Method for Non-convex Multi-objective Optimization Problems Adhikary, Bikram Ansary, Md Abu Talhamainuddin Treanta, Savin Optimization and Control 90C29, 90C26, 65K10, 49M99 In this paper, we develop a global descent method for non-convex multi-objective optimization problems. The proposed approach builds upon foundational concepts from single-objective global descent techniques while removing the need for predefined scalars or ordering information of objective functions. Initially, the proposed method identifies a local weak efficient solution using any suitable descent algorithm, then applies an auxiliary function termed the multi-objective global descent function to systematically transition toward improved local weak efficient solutions. It is justified that this method can generate a global Pareto front for non-convex problems, which has many different local Pareto fronts. Finally, comprehensive numerical experiments on benchmark non-convex multi-objective optimization problems have been done to demonstrate the method's robustness, scalability and effectiveness of the proposed method. |
| title | Global Descent Method for Non-convex Multi-objective Optimization Problems |
| topic | Optimization and Control 90C29, 90C26, 65K10, 49M99 |
| url | https://arxiv.org/abs/2507.22390 |