Cutting plane oracles for non-smooth trust-regions

Abstract

We prove global convergence of a bundle trust region algorithm for non-smooth non-convex optimization, where cutting planes are generated by oracles respecting four basic rules. The benefit is that convergence theory applies to a large variety of methods encountered in practice. This includes in particular the method of downshifted tangents, for which previously no convergence result in the trust region framework was known. We also show that certain splitting techniques can be seen as special cases of bundle trust region techniques.