Penalty decomposition derivative free method for the minimization of partially separable functions over a convex feasible set
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911507358416896 |
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| author | Cecere, Francesco Lapucci, Matteo Pucci, Davide Sciandrone, Marco |
| author_facet | Cecere, Francesco Lapucci, Matteo Pucci, Davide Sciandrone, Marco |
| contents | In this paper, we consider the problem of minimizing a smooth function, given as finite sum of black-box functions, over a convex set. In order to advantageously exploit the structure of the problem, for instance when the terms of the objective functions are partially separable, noisy, costly or with first-order information partially accessible, we propose a framework where the penalty decomposition approach is combined with a derivative-free line-search-based method. Under standard assumptions, we state theoretical results showing that the proposed algorithm is well-defined and globally convergent to stationary points. The results of preliminary numerical experiments, performed on test problems with number of variables up to thousands, show the validity of the proposed method w.r.t. state of the art methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Penalty decomposition derivative free method for the minimization of partially separable functions over a convex feasible set Cecere, Francesco Lapucci, Matteo Pucci, Davide Sciandrone, Marco Optimization and Control 90C56, 90C30, 90C26 In this paper, we consider the problem of minimizing a smooth function, given as finite sum of black-box functions, over a convex set. In order to advantageously exploit the structure of the problem, for instance when the terms of the objective functions are partially separable, noisy, costly or with first-order information partially accessible, we propose a framework where the penalty decomposition approach is combined with a derivative-free line-search-based method. Under standard assumptions, we state theoretical results showing that the proposed algorithm is well-defined and globally convergent to stationary points. The results of preliminary numerical experiments, performed on test problems with number of variables up to thousands, show the validity of the proposed method w.r.t. state of the art methods. |
| title | Penalty decomposition derivative free method for the minimization of partially separable functions over a convex feasible set |
| topic | Optimization and Control 90C56, 90C30, 90C26 |
| url | https://arxiv.org/abs/2503.21631 |