Convergence of an Inexact Algorithm for Composite Nonsmooth Optimization

We describe an inexact version of Fletcher's second-order correction algorithm for minimizing composite nondifferentiable functions, and add a test which allows global convergence to be demonstrated without the assumption that a global minimum of the model function is found at each iteration. Implementable criteria for accepting inexact solutions of the subproblem, while retaining local convergence properties, are also given.