Globally convergent BFGS method for nonsmooth convex optimization

We propose an implementable BFGS method for solving a nonsmooth convex optimization problem by converting the original objective function into a once continuously differentiable function by way of the Moreau-Yosida regularization. The proposed method makes use of approximate function and gradient values of the Moreau-Yosida regularization instead of the corresponding exact values. We prove the global convergence of the proposed method under the assumption of strong convexity of the objective function.