Proximal Regularization for the Saddle Point Gradient Dynamics

This article concerns the solution of a convex optimization problem through the saddle point gradient dynamics. Instead of using the standard Lagrangian as is classical in this method, we consider a regularized Lagrangian obtained through a proximal minimization step. We show that, without assumptions of smoothness or strict convexity in the original problem, the regularized Lagrangian is smooth a...