30 research outputs found
Strict pseudocontractions and demicontractions, their properties and applications
We give properties of strict pseudocontractions and demicontractions defined
on a Hilbert space, which constitute wide classes of operators that arise in
iterative methods for solving fixed point problems. In particular, we give
necessary and sufficient conditions under which a convex combination and
composition of strict pseudocontractions as well as demicontractions that share
a common fixed point is again a strict pseudocontraction or a demicontraction,
respectively. Moreover, we introduce a generalized relaxation of composition of
demicontraction and give its properties. We apply these properties to prove the
weak convergence of a class of algorithms that is wider than the
Douglas-Rachford algorithm and projected Landweber algorithms. We have also
presented two numerical examples, where we compare the behavior of the
presented methods with the Douglas-Rachford method.Comment: 27 pages, 3 figure
Obtuse cones and Gram matrices with nonnegative inverse
AbstractWe study some properties of Gram matrices with nonnegative inverse which lead to the constructions of obtuse cones. These constructions can find applications in optimization problems, e.g., in methods of convex feasibility problems or of convex minimization problems
An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space
This paper is concerned with the variational inequality problem (VIP) over
the fixed point set of a quasi-nonexpansive operator. We propose, in
particular, an algorithm which entails, at each step, projecting onto a
suitably chosen half-space, and prove that the sequences it generates converge
to the unique solution of the VIP. We also present an application of our result
to a hierarchical optimization problem.Comment: Accepted for publication in Numerical Functional Analysis and
Optimizatio
My艣l i polityka: ksi臋ga pami膮tkowa dedykowana profesorowi Jackowi Marii Majchrowskiemu T. 2
Publikacja jubileuszowa z okazji 40-lecia pracy naukowej profesora Jacka Majchrowskieg