We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing. We are motivated by the problem of restoring noisy and blurry images via variational methods, by using total variation regularization. We obtain rigorous convergence results, and effective stopping criteria for the gener...

We present a Neumann-subproblem a posteriori "nite element procedure for the e$cient and accurate calculation of rigorous, `constant-freea upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial di!erential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori "nite element procedure is described; the asymp...

In order to generate valid convex lower bounding problems for noncon-vex twice{diierentiable optimization problems, a method that is based on second{ order information of general twice{diierentiable functions is presented. Using interval Hessian matrices, valid lower bounds on the eigenvalues of such functions are obtained and used in constructing convex underestimators. By solving several non-...

In this contribution, a systematic procedure for control structure selection based on rigorous models is presented. The basic idea is that a feedback controller that regulates certain measurable quantities to their set-points should steer the process towards its economic optimum in the presence of disturbances and model uncertainties. This part of the analysis is performed for the stationary be...