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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2605.09361 |
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| _version_ | 1866909030100762624 |
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| author | Li, Guoping Song, Wen |
| author_facet | Li, Guoping Song, Wen |
| contents | A nonlinear kernel-free soft quadratic surface support vector machine model with 0-1 loss function ($L_{0/1}$-SQSSVM) is proposed for binary classification problems, which is non-convex discontinuous. We are devoted to establishing the first and the second-order optimality conditions for the $L_{0/1}$-SQSSVM. We establish a stationary equation using the properties of proximal operator of 0-1 loss function. We design a Newton method based on the stationary equation to solve $L_{0/1}$-SQSSVM model and prove that the Newton method has local quadratic convergence under the second-order sufficient condition. Numerical experience on artificial datasets and benchmark datasets demonstrate that the Newton method for $L_{0/1}$-SQSSVM achieves higher classification accuracy with less CPU time cost than other state-of-the-art methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09361 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Newton Method for Soft Quadratic Surface Support Vector Machine with 0-1 Loss Function Li, Guoping Song, Wen Optimization and Control A nonlinear kernel-free soft quadratic surface support vector machine model with 0-1 loss function ($L_{0/1}$-SQSSVM) is proposed for binary classification problems, which is non-convex discontinuous. We are devoted to establishing the first and the second-order optimality conditions for the $L_{0/1}$-SQSSVM. We establish a stationary equation using the properties of proximal operator of 0-1 loss function. We design a Newton method based on the stationary equation to solve $L_{0/1}$-SQSSVM model and prove that the Newton method has local quadratic convergence under the second-order sufficient condition. Numerical experience on artificial datasets and benchmark datasets demonstrate that the Newton method for $L_{0/1}$-SQSSVM achieves higher classification accuracy with less CPU time cost than other state-of-the-art methods. |
| title | Newton Method for Soft Quadratic Surface Support Vector Machine with 0-1 Loss Function |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.09361 |