Errors in the data and the forward operator of an inverse problem can be handily modelled using partial order in Banach lattices. We present some existing results of the theory of regularisation in this novel framework, ...

We are presenting a modification of the well-known Alternating Direction Method of Multipliers (ADMM) algorithm with additional preconditioning that aims at solving convex optimisation problems with nonlinear operator ...

We derive stability criteria for saddle points of a class of nonsmooth optimization problems in Hilbert spaces arising in PDE-constrained optimization, using metric regularity of infinite-dimensional set-valued mappings. ...