A Decomposition Algorithm for Convex Nondifferentiable Minimization with Errors

Abstract

A decomposition algorithm based on proximal bundle-type method with inexact data is presented for minimizing an unconstrained nonsmooth convex function $f$. At each iteration, only the approximate evaluation of $f$ and its approximate subgradients are required which make the algorithm easier to implement. 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. Numerical tests emphasize the theoretical findings.