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

Document Type : Research Paper


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


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.


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Volume 14, Issue 8
August 2023
Pages 197-215
  • Receive Date: 03 March 2021
  • Revise Date: 20 May 2021
  • Accept Date: 29 May 2021