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Gradient projection algorithms for optimization problems on convex sets and application to SVM | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 19، دوره 14، شماره 8، آبان 2023، صفحه 197-215 اصل مقاله (857.4 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23460.2543 | ||
| نویسندگان | ||
| Radhia Bessi1؛ Harouna Soumare* 2 | ||
| 1The Laboratory of Mathematical Modelling and Numeric in Engineering Sciences, National Engineering School of Tunis, University of Tunis El Manar, Rue B\'echir Salem Belkhiria Campus Universitaire, B.P. 37, 1002 Tunis Belvedere, Tunisia | ||
| 2The Laboratory of Mathematical Modelling and Numeric in Engineering Sciences, National Engineering School of Tunis, University of Tunis El Manar, Rue Bechir Salem Belkhiria Campus universitaire, B.P. 37, 1002 Tunis Belvédère, Tunisia | ||
| تاریخ دریافت: 13 اسفند 1399، تاریخ بازنگری: 30 اردیبهشت 1400، تاریخ پذیرش: 08 خرداد 1400 | ||
| چکیده | ||
| In this paper, we present some gradient projection algorithms for solving optimization problems with a convex-constrained set. We derive the optimality condition when the convex set is a cone and under some mild assumptions, we prove the convergence of these algorithms. Finally, we apply them to quadratic problems arising in training support vector machines for the Wisconsin Diagnostic Breast Cancer (WDBC) classification problem. | ||
| کلیدواژهها | ||
| Optimization on convex cones؛ projection algorithm؛ generalized gradient projection algorithm؛ Euler inequation؛ quadratic optimization problem؛ Lipschitz continuous gradient؛ soft and hard dual SVM problem؛ classification of breast cancer | ||
| مراجع | ||
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