Regularisation, optimisation, subregularity

Abstract Regularisation theory in Banach spaces, and non-norm-squared regularisation even finite dimensions, generally relies upon Bregman divergences to replace norm convergence. This is comparable the extension of first-order optimisation methods spaces. can, however, be somewhat suboptimal terms descriptiveness. Using concept ( strong ) metric subregularity , previously used prove fast local convergence methods, we show spaces for regularisation. For problems such as total variation regularised image reconstruction, reduces a geometric condition on ground truth: flat areas truth have compensate fidelity term not having second-order growth within kernel forward operator. Our approach proving results based formulations inverse problems. As side result that develop, provide complexity methods: how many steps N δ algorithm do take approximate solutions converge corruption level ↘ 0?