8,431 research outputs found
Best Approximation from the Kuhn-Tucker Set of Composite Monotone Inclusions
Kuhn-Tucker points play a fundamental role in the analysis and the numerical
solution of monotone inclusion problems, providing in particular both primal
and dual solutions. We propose a class of strongly convergent algorithms for
constructing the best approximation to a reference point from the set of
Kuhn-Tucker points of a general Hilbertian composite monotone inclusion
problem. Applications to systems of coupled monotone inclusions are presented.
Our framework does not impose additional assumptions on the operators present
in the formulation, and it does not require knowledge of the norm of the linear
operators involved in the compositions or the inversion of linear operators
A Besov algebra calculus for generators of operator semigroups and related norm-estimates
We construct a new bounded functional calculus for the generators of bounded
semigroups on Hilbert spaces and generators of bounded holomorphic semigroups
on Banach spaces. The calculus is a natural (and strict) extension of the
classical Hille-Phillips functional calculus, and it is compatible with the
other well-known functional calculi. It satisfies the standard properties of
functional calculi, provides a unified and direct approach to a number of
norm-estimates in the literature, and allows improvements of some of them.Comment: This is the authors' accepted version of a paper which will be
published in Mathematische Annale
Local Analysis of Inverse Problems: H\"{o}lder Stability and Iterative Reconstruction
We consider a class of inverse problems defined by a nonlinear map from
parameter or model functions to the data. We assume that solutions exist. The
space of model functions is a Banach space which is smooth and uniformly
convex; however, the data space can be an arbitrary Banach space. We study
sequences of parameter functions generated by a nonlinear Landweber iteration
and conditions under which these strongly converge, locally, to the solutions
within an appropriate distance. We express the conditions for convergence in
terms of H\"{o}lder stability of the inverse maps, which ties naturally to the
analysis of inverse problems
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