The authors present a method for solving the nondifferentiable convex programming problem: subject to , where is a nondifferentiable convex function. The method is developed using the ideas of the Moreau-Yosida regularization [K. Yosida, Functional analysis (1965; Zbl 0126.11504)], the bundle method, and the quasi-Newton method. It is shown that in this method the minimizing solution of the given programming problem is exactly the solution of a subproblem of minimizing the Moreau-Yosida regularization of over .
The entire discussion in the paper is devoted to the solution of the subproblem, and a globally and superlinearly convergent quasi-Newton bundle-type algorithm is described for solving the subproblem.
No numerical results are given.