Natural image statistics indicate that we should use non-convex norms for most regularization tasks in image processing and computer vision. Still, they are rarely used in practice due to the challenge of optimization. Recently, iteratively reweighed `1 minimization (IRL1) has been proposed as a way to tackle a class of non-convex functions by solving a sequence of convex `2-`1 problems. We ext...

We propose a general method to determine the theoretical microstructure in one dimensional elastic bars whose internal deformation energy is given by non-convex polynomials. We use non-convex variational principles and Young measure theory to describe the optimal energetic configuration of the body. By using convex analysis and classical characterizations of algebraic moments, we can formulate ...

In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of fourkinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.Furthermore, the notion of the degree to which an $L$-subset of an $L$-ord...