A 3D slip-dependent frictional contact problem in elastostatics is discussed. We deliver a variational formulation as a mixed variational problem whose Lagrange multipliers set is solutiondependent. Then, the existence and the boundedness of the solutions is investigated. The proof is based on a recent result for an abstract mixed variational problem with solution-dependent set of Lagrange mult...

We propose a variational framework for the integration multiple competing shape priors into level set based segmentation schemes. By optimizing an appropriate cost functional with respect to both a level set function and a (vector-valued) labeling function, we jointly generate a segmentation (by the level set function) and a recognition-driven partition of the image domain (by the labeling func...

An explicit hierarchical fixed point algorithm is introduced to solve the monotone variational inequality over the fixed point set of a nonexpansive mapping. This paper discusses a monotone variational inequality with variational constraint and convex optimization problems over the fixed point set of a nonexpansive mapping. The strong convergence for the proposed algorithm to the solution is gu...

In this paper, we propose a novel region-based active contour model in a variational level set formulation. The energy functional for the proposed model consists of two terms, i.e., global term, local term. Therefore, the combination of these two forces allows for flexible initialization of the contours. This energy is then incorporated into a level set formulation with a level set regularizati...

We derive the Euler-Lagrange equations for minimizers of causal variational principles in the non-compact setting with constraints, possibly prescribing symmetries. Considering first variations, we show that the minimizing measure is supported on the intersection of a hyperplane with a level set of a function which is homogeneous of degree two. Moreover, we perform second variations to obtain t...

In this work we consider the problem of parameter learning for variational image denoising models. The learning problem is formulated as a bilevel optimization problem, where the lower level problem is given by the variational model and the higher level problem is expressed by means of a loss function that penalizes errors between the solution of the lower level problem and the ground truth dat...