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

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.

Keywords:

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