Broyden quasi-Newton secant-type method for solving constrained mixed generalized equations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866910865206280192 |
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| author | Junior, P. C. da Silva Ferreira, O. P. Silva, G. N. |
| author_facet | Junior, P. C. da Silva Ferreira, O. P. Silva, G. N. |
| contents | This paper presents a novel variant of the Broyden quasi-Newton secant-type method aimed at solving constrained mixed generalized equations, which can include functions that are not necessarily differentiable. The proposed method integrates the classical secant approach with techniques inspired by the Conditional Gradient method to handle constraints effectively. We establish local convergence results by applying the contraction mapping principle. Specifically, under assumptions of Lipschitz continuity, a modified Broyden update for derivative approximation, and the metric regularity property, we show that the algorithm generates a well-defined sequence that converges locally at a Q-linear rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06206 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Broyden quasi-Newton secant-type method for solving constrained mixed generalized equations Junior, P. C. da Silva Ferreira, O. P. Silva, G. N. Optimization and Control 65K15, 49M15, 90C30 This paper presents a novel variant of the Broyden quasi-Newton secant-type method aimed at solving constrained mixed generalized equations, which can include functions that are not necessarily differentiable. The proposed method integrates the classical secant approach with techniques inspired by the Conditional Gradient method to handle constraints effectively. We establish local convergence results by applying the contraction mapping principle. Specifically, under assumptions of Lipschitz continuity, a modified Broyden update for derivative approximation, and the metric regularity property, we show that the algorithm generates a well-defined sequence that converges locally at a Q-linear rate. |
| title | Broyden quasi-Newton secant-type method for solving constrained mixed generalized equations |
| topic | Optimization and Control 65K15, 49M15, 90C30 |
| url | https://arxiv.org/abs/2503.06206 |