A new multidimensional optimization problem is considered in the tropical mathematics setting. The problem is to minimize a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield and given by a conjugate transposition operator. A special case of the problem, which arises in just-in-time scheduling, serves as a motivation for the study. To solve the general pr...

This paper derives analytical estimates for the rates of convergence of numerical first and second derivative operators involved in flux reconstruction (FR). These estimates yield the rate of convergence for steady-state advection-diffusion problems when error is measured in the vector seminorm induced by the advection-diffusion operator. This serves to rigorously quantify the effect of polynom...

When deriving rates of convergence for the approximations generated by the application of Tikhonov regularization to ill–posed operator equations, assumptions must be made about the nature of the stabilization (i.e., the choice of the seminorm in the Tikhonov regularization) and the regularity of the least squares solutions which one looks for. In fact, it is clear from works of Hegland, Engl a...

We establish theoretical convergence results for an Iteratively Regularized Gauss Newton (IRGN) algorithm with a specific Tikhonov regularization. This Tikhnov regularization, which uses a seminorm generated by a linear operator, is motivated by mapping of the minimization variables to physical space which exposes the different scales of the parameters and therefore also suggests appropriate we...

We extend some previous results of ours [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous estimates in terms of the Euclidean norm. For example, one can use as a separating family of seminorms the absolute values of the components of the actions: with ...

In this papers we analyze the minimization of seminorms ‖L · ‖ on R under the constraint of a bounded I-divergence D(b,H ·) for rather general linear operators H and L. The I-divergence is also known as Kullback-Leibler divergence and appears in many models in imaging science, in particular when dealing with Poisson data. Often H represents, e.g., a linear blur operator and L is some discrete d...

In this paper we prove a fractional analogue of the classical Korn's first inequality. The inequality makes it possible to show equivalence function space vector field characterized by Gagliardo-type seminorm with 'projected difference' that corresponding Sobolev space. As an application, will use obtain Caccioppoli-type for nonlinear system nonlocal equations, which in turn is key ingredient a...

We analyze the asymptotic convergence of all infinite products of matrices taken in a given finite set by looking only at finite or periodic products. It is known that when the matrices of the set have a common nonincreasing polyhedral norm, all infinite products converge to zero if and only if all infinite periodic products with periods smaller than a certain value converge to zero. Moreover, ...

A mathematical analysis is presented for a class of interior penalty (IP) discontinuous Galerkin approximations of elliptic boundary value problems. In the framework of the present theory one can derive some overpenalized IP bilinear forms avoiding the notion of fluxes and artificial penalty terms. The main idea is to start from bilinear forms for the local average of discontinuous approximatio...

In this paper we analyze, mainly in a finitary setting, the consistency properties of fuzzy possibilities, interpreting them as instances of upper previsions and applying the basic notions of avoiding sure loss and coherence from the theory of imprecise probabilities. It ensues that fuzzy possibilities always avoid sure loss, but satisfy the stronger coherence condition only in a special case. ...