Direct-search methods in the year 2025: Theoretical guarantees and algorithmic paradigms
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908393747251200 |
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| author | Dzahini, K. J. Rinaldi, F. Royer, C. W. Zeffiro, D. |
| author_facet | Dzahini, K. J. Rinaldi, F. Royer, C. W. Zeffiro, D. |
| contents | Optimizing a function without using derivatives is a challenging paradigm, that precludes from using classical algorithms from nonlinear optimization, and may thus seem intractable other than by using heuristics. Nevertheless, the field of derivative-free optimization has succeeded in producing algorithms that do not rely on derivatives and yet are endowed with convergence guarantees. One class of such methods, called direct-search methods, is particularly popular thanks to its simplicity of implementation, even though its theoretical underpinnings are not always easy to grasp.
In this work, we survey contemporary direct-search algorithms from a theoretical viewpoint, with the aim of highlighting the key theoretical features of these methods. \rev{We provide a basic introduction to the main classes of direct-search methods, including line-search techniques that have received little attention in earlier surveys. We also put a particular emphasis on probabilistic direct-search techniques and their application to noisy problems, a topic that has undergone significant algorithmic development in recent years. Finally, we complement existing surveys by reviewing the main theoretical advances for solving constrained and multiobjective optimization using direct-search algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_05322 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Direct-search methods in the year 2025: Theoretical guarantees and algorithmic paradigms Dzahini, K. J. Rinaldi, F. Royer, C. W. Zeffiro, D. Optimization and Control Optimizing a function without using derivatives is a challenging paradigm, that precludes from using classical algorithms from nonlinear optimization, and may thus seem intractable other than by using heuristics. Nevertheless, the field of derivative-free optimization has succeeded in producing algorithms that do not rely on derivatives and yet are endowed with convergence guarantees. One class of such methods, called direct-search methods, is particularly popular thanks to its simplicity of implementation, even though its theoretical underpinnings are not always easy to grasp. In this work, we survey contemporary direct-search algorithms from a theoretical viewpoint, with the aim of highlighting the key theoretical features of these methods. \rev{We provide a basic introduction to the main classes of direct-search methods, including line-search techniques that have received little attention in earlier surveys. We also put a particular emphasis on probabilistic direct-search techniques and their application to noisy problems, a topic that has undergone significant algorithmic development in recent years. Finally, we complement existing surveys by reviewing the main theoretical advances for solving constrained and multiobjective optimization using direct-search algorithms. |
| title | Direct-search methods in the year 2025: Theoretical guarantees and algorithmic paradigms |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.05322 |