A Regularized Gradient Projection Method for the Minimization Problem

Abstract

We investigate the following regularized gradient projectionalgorithm $x_{n+\text{1}}=P_c\left(I-{\gamma }_n\left(\nabla f+{\alpha }_{n}I\right)\right)x_n$, $n\ge \text{0}$. Under some different control conditions, we prove that this gradient projection algorithmstrongly converges to the minimum norm solution of the minimization problem ${\text{min}}_{x\in C}f\left(x\right)$.