Minimization of Tikhonov Functionals in Banach Spaces

A forward-backward splitting algorithm for the minimization of non-smooth convex functionals in Banach space

We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert space, we propose a generalization which involves the iterative solution of simpler subproblems. Descent and convergence properties of this new algorithm are...

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

Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities

In this paper, we enlighten the role of variational inequalities for obtaining convergence rates in Tikhonov regularization of nonlinear ill-posed problems with convex penalty functionals under convexity constraints in Banach spaces. Variational inequalities are able to cover solution smoothness and the structure of nonlinearity in a uniform manner, not only for unconstrained but, as we indicat...

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

In this paper, we show that the additive Schwarz method proposed in [3] to solve one-obstacle problems converges in a much more general framework. We prove that this method can be applied to the minimization of functionals over a general enough convex set in a reflexive Banach space. In the Sobolev spaces, the proposed method is an additive Schwarz method for the solution of the variational ine...

Minimization of Nonsmooth Convex Functionals in Banach Spaces

We develop a uniied framework for convergence analysis of subgradient and subgradient projection methods for minimization of nonsmooth convex functionals in Banach spaces. The important novel features of our analysis are that we neither assume that the functional is uniformly or strongly convex, nor use regularization techniques. Moreover, no boundedness assumptions are made on the level sets o...