Multi-parameter Tikhonov Regularisation in Topological Spaces

Abstract: We study the behaviour of Tikhonov regularisation on topological spaces with multiple regularisation terms. The main result of the paper shows that multi-parameter regularisation is well-posed in the sense that the results depend continuously on the data and converge to a true solution of the equation to be solved as the noise level decreases to zero. Moreover, we derive convergence rates in terms of a generalised Bregman distance using the method of variational inequalities. All the results in the paper, including the convergence rates, consider not only noise in the data, but also errors in the operator.