An ODE-like nonmonotone method for nonsmooth convex optimization.

Based on the Moreau-Yosida regularization and a modified nonmonotone line search technique, this paper presents an implementable ordinary differentiable equation-like method for solving a possibly nondifferentiable convex minimization problem by converting the original objective function to a once continuously differentiable function. The proposed method makes use of approximate function and gradient values of the Moreau-Yosida regularization instead of the corresponding exact values. Under some reasonable conditions, the proposed method is shown to be globally and superlinearly convergent. Some preliminary numerical results are also reported to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]