The infimal Heegaard gradient of a compact 3-manifold was defined and studied by Marc Lackenby in an approach toward the well-known virtually Haken conjecture. As instructive examples, we consider Seifert fibered 3-manifolds, and show that a Seifert fibered 3-manifold has zero infimal Heegaard gradient if and only if it it virtually fibers over the circle or over a surface other than the 2-sphe...

In this paper, a primal-dual algorithm for total bounded variation (TV)–type image restoration is analyzed and tested. Analytically it turns out that employing a global Lregularization, with 1 < s ≤ 2, in the dual problem results in a local smoothing of the TVregularization term in the primal problem. The local smoothing can alternatively be obtained as the infimal convolution of the r-norm, wi...

The infimal convolution of total (generalized) variation type functionals and its application as regularization for video and image reconstruction is considered. The definition of this particular type of regularization functional is motivated by the need of suitably combining spatial and temporal regularity requirements for video processing. The proposed functional is defined in an infinite dim...

We propose a unifying framework that combines smoothing approximation with fast first order algorithms for solving nonsmooth convex minimization problems. We prove that independently of the structure of the convex nonsmooth function involved, and of the given fast first order iterative scheme, it is always possible to improve the complexity rate and reach an O(ε−1) efficiency estimate by solvin...

We study a framework for constructing coherent and convex measures of risk that is inspired by infimal convolution operator, and which is shown to constitute a new general representation of these classes of risk functions. We then discuss how this scheme may be effectively applied to obtain a class of certainty equivalent measures of risk that can directly incorporate preferences of a rational ...

We study a question posed by Stephen Simons in his 2008 monograph involving “bigger conjugate” (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the state-of-the-art of harder problems in monotone operator theory, especially the sum problem. In this paper, we provide some tools fo...