Gradient projection algorithms for optimization problems on convex sets and application to SVM

نویسندگان
Bessi, Radhia ID 1
Soumare, Harouna ID 2

1 The 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

2 The 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

doi
10.22075/ijnaa.2021.23460.2543
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