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We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are...
The Least Action Principle is the simplest and the most nature rule in the world. Using variational minimizing methods and the implicit symmetries, we prove the existence of the odd symmetric paraboli...
Abstract: Motivated by the recent work on conditional risk measures, this paper studies the Ekeland's variational principle for a proper, lower semicontinuous and lower bounded $\bar{L}^{0}-$valued fu...
We investigate higher-order geometric k-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images,e.g., in longitudinal ...
A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing mea...
We investigate higher-order geometric k-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudin...
We generalize a family of variation norm estimates (Theorem 1.1) of L´epingle with endpoint estimates of Bourgain and Pisier-Xu to a family of variational estimates for paraproducts (Theorem 1....
We prove an implicit function theorem for functions on infinite dimensional Banach manifolds, invariant under the (local) action of a finite dimensional Lie group. Motivated by some geometric variatio...
We propose a new variational problem which we call the Split Variational Inequality Problem (SVIP). It entails finding a solution of one Variational Inequality Problem (VIP), the image of which under ...
In this paper we develop new applications of variational analysis and generalized differ- entiation to the following optimization problem and its specifications: given n closed subsets of a Banach sp...
As a simple model for lattice defects like grain boundaries in solid state physics we consider potentials which are obtained from a periodic potential V = V (x, y) on R2 with period lattice Z2 by sett...
This paper develops a rst-order system least-squares (FOSLS) formulation for equations of two-phase ow. The main goal is to show that this discretization, along with numerical techniques such as nes...

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