Worst-case complexity analysis of derivative-free methods for multi-objective optimization
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909621069807616 |
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| author | Liuzzi, Giampaolo Lucidi, Stefano |
| author_facet | Liuzzi, Giampaolo Lucidi, Stefano |
| contents | In this work, we are concerned with the worst case complexity analysis of "a posteriori" methods for unconstrained multi-objective optimization problems where objective function values can only be obtained by querying a black box. We present two main algorithms, namely DFMOnew and DFMOlight which are based on a linesearch expansion technique. In particular, \DFMOnew, requires a complete exploration of the points in the current set of non-dominated solutions, whereas DFMOlight only requires the exploration around a single point in the set of non-dominated solutions. For these algorithms, we derive worst case iteration and evaluation complexity results. In particular, the complexity results for DFMOlight aligns with those recently proved in the literature for a directional multisearch method. Furthermore, exploiting an expansion technique of the step, we are also able to give further complexity results concerning the number of iterations with a measure of stationarity above a prefixed tolerance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Worst-case complexity analysis of derivative-free methods for multi-objective optimization Liuzzi, Giampaolo Lucidi, Stefano Optimization and Control 90C29, 90C30, 90C56 In this work, we are concerned with the worst case complexity analysis of "a posteriori" methods for unconstrained multi-objective optimization problems where objective function values can only be obtained by querying a black box. We present two main algorithms, namely DFMOnew and DFMOlight which are based on a linesearch expansion technique. In particular, \DFMOnew, requires a complete exploration of the points in the current set of non-dominated solutions, whereas DFMOlight only requires the exploration around a single point in the set of non-dominated solutions. For these algorithms, we derive worst case iteration and evaluation complexity results. In particular, the complexity results for DFMOlight aligns with those recently proved in the literature for a directional multisearch method. Furthermore, exploiting an expansion technique of the step, we are also able to give further complexity results concerning the number of iterations with a measure of stationarity above a prefixed tolerance. |
| title | Worst-case complexity analysis of derivative-free methods for multi-objective optimization |
| topic | Optimization and Control 90C29, 90C30, 90C56 |
| url | https://arxiv.org/abs/2505.17594 |