A proximal bundle method with inexact data for convex nondifferentiable minimization

Abstract

A proximal bundle method with inexact data is presented for minimizing an unconstrained nonsmooth convex function f . At each iteration, only the approximate evaluations of f and its ε -subgradients are required and its search directions are determined via solving quadratic programmings. Compared with the pre-existing results, the polyhedral approximation model that we offer is more precise and a new term is added into the estimation term of the descent from the model. It is shown that every cluster of the sequence of iterates generated by the proposed algorithm is an exact solution of the unconstrained minimization problem.