Conjugate gradient type methods for the nondifferentiable convex minimization

We proposed implementable conjugate gradient type methods for solving a possibly nondifferentiable convex minimization problem by converting the original objective function to a once continuously differentiable function by way of the Moreau-Yosida regularization. The proposed methods make use of approximate function and gradient values of the Moreau-Yosida regularization instead of the corresponding exact values. The global convergence is established under mild conditions.