An Additive Schwarz Method for the Constrained Minimization of Functionals in Reflexive Banach Spaces

Convergence rate analysis of an asynchronous space decomposition method for convex Minimization

We analyze the convergence rate of an asynchronous space decomposition method for constrained convex minimization in a reflexive Banach space. This method includes as special cases parallel domain decomposition methods and multigrid methods for solving elliptic partial differential equations. In particular, the method generalizes the additive Schwarz domain decomposition methods to allow for as...

Multigrid methods for variational inequalities

In this paper we introduce four multigrid algorithms for the constrained minimization of non-quadratic functionals. The algorithm introduced in [L. Badea, Convergence rate of a Schwarz multilevel method for the constrained minimization of non-quadratic functionals, SIAM J. Numer. Anal., 44, 2, 2006, p. 449-477], has a sub-optimal computing complexity because the convex set, which is defined on ...

Weakly almost periodic functionals, representations, and operator spaces

A theorem of Davis, Figiel, Johnson and Pe lczyński tells us that weakly-compact operators between Banach spaces factor through reflexive Banach spaces. The machinery underlying this result is that of the real interpolation method, which has been adapted to the category of operator spaces by Xu, showing the this factorisation result also holds for completely bounded weakly-compact maps. In this...

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

Existence of three solutions for a class of fractional boundary value systems

In this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. These problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive Banach space. To make the nonlinear methods work, some careful analysis of t...