Closed convex sets for which the barrier cone has a nonempty interior, as well as proper extended-values real functionals for which the domain of their Fenchel conjugate is nonempty, are mathematical objects currently encountered in various areas of optimization theory and variational analysis (see for instance the class of well-behaved functions introduced by Auslender and Crouzeix in [5]). Th...

In the present paper we prove the Chebyshev inequality involving two isotonic linear functionals. Namely, if A and B are isotonic linear functionals, then A(p f g)B(q)+A(p)B(q f g) A(p f )B(qg) + A(pg)B(q f ) , where p,q are non-negative weights and f ,g are similarly ordered functions such that the above-mentioned terms are well-defined. If functionals are equal, i.e. A = B and if p = q , then...

The optimal control problems for stationary magnetohydrodynamic equations under the inhomogeneous mixed boundary conditions a magnetic field and Dirichlet condition velocity are considered. role of controls in study is played by normal tangential components given on different parts exterior current density. Quadratic tracking-type functionals velocity, or pressure taken as cost functionals. glo...

A general price process represented by a two-component Markov process is considered. Its first component is interpreted as a price process and the second one as an index process modulating the price component. American type options with pay-off functions, which admit power type upper bounds, are studied. Both the transition characteristics of the price processes and the payoff functions are ass...

In this work we extend the results of [2] to a family of abstract functionals of autonomous type satisfying suitable locality and additivity properties, and general integral growth conditions of superlinear type. We single out a condition which is necessary and sufficient in order for a functional of this class to admit an integral representation, and sufficient as well to have an integral repr...

The paper addresses the stability problem of linear time delay system. In the literature, the most popular approach to tackle this problem relies on the use of LyapunovKrasovskii functionals. Many results have proposed new functionals and techniques for deriving less and less conservative stability conditions. Nevertheless, all these approaches use the same trick, the well-known Jensen’s inequa...

In this paper we discuss two approaches to evolutionary Γ-convergence of gradient systems in Hilbert spaces. The formulation of the gradient system is based on two functionals, namely the energy functional and the dissipation potential, which allows us to employ Γ-convergence methods. In the first approach we consider families of uniformly convex energy functionals such that the limit passage o...

We study variational methods of bounded variation type for the data analysis. Y. Meyer characterized minimizers of the Rudin-Osher-Fatemi functional in dependence of the G-norm of the data. These results and the follow up work on this topic are generalized to functionals defined on spaces of functions with derivatives of finite bounded variation. In order to derive a characterization of minimiz...

Motivated by asymptotic problems in the theory of empirical processes, and specifically by tests of independence, we study the law of quadratic functionals of the (weighted) Brownian sheet and of the bivariate Brownian bridge on [0, 1]. In particular: (i) we use Fubini type techniques to establish identities in law with quadratic functionals of other Gaussian processes, (ii) we explicitly calcu...

Motivated by optimal investment problems in mathematical finance, we consider a variational problem of Neyman–Pearson type for law-invariant robust utility functionals and convex risk measures. Explicit solutions are found for quantile-based coherent risk measures and related utility functionals. Typically, these solutions exhibit a critical phenomenon: If the capital constraint is below some c...