The analysis of the bearing capacity of structures with a rigid-plastic behaviour can be achieved resorting to computational limit analysis. Recent techniques have allowed scientists and engineers to determine upper and lower bounds of the load factor under which the structure will collapse. Despite the attractiveness of these results, their application to practical examples is still hampered by the size of the resulting optimisation process.
joint work with Sung Ha Kang
In this talk, I present numerical methods for solving Euler's elastica-regularized model for image processing. The minimizing functional is non-smooth and non-convex, due to the presence of a curvature term, which makes this model more powerful than the total variation-based models. Theoretical analysis as well as various numerical results in image processing and medical image reconstruction will be presented.
joint work with Roland Herzog, Ronny Bergmann, Daniel Tenbrinck
This talk introduces a new duality theory that generalizes the classical Fenchel-Legendre conjugation to functions defined on Riemannian manifolds. We present that results from convex analysis also hold for this novel duality theory on manifolds. Especially the Fenchel--Moreau theorem and properties involving the Riemannian subdifferential can be stated in this setting. A main application of this theory is that a specific class of optimization problems can be rewritten into a primal-dual saddle-point formulation. This is a first step towards efficient algorithms.