Krasnoselskii-Mann Iterations: Inertia, Perturbations and Approximation

This paper is concerned with the study of a family of fixed point iterations combining relaxation with different inertial (acceleration) principles. We provide a systematic, unified and insightful analysis of the hypotheses that ensure their weak, strong and linear convergence, either matching or improving previous results obtained by analysing particular cases separately. We also show … Read more

Data-compatibility of algorithms

The data-compatibility approach to constrained optimization, proposed here, strives to a point that is “close enough” to the solution set and whose target function value is “close enough” to the constrained minimum value. These notions can replace analysis of asymptotic convergence to a solution point of infinite sequences generated by specific algorithms. We consider a … Read more

Best approximation to common fixed points of a semigroup of nonexpansive operators

We study a sequential algorithm for finding the projection of a given point onto the common fixed points set of a semigroup of nonexpansive operators in Hilbert space. The convergence of such an algorithm was previously established only for finitely many nonexpansive operators. Algorithms of this kind have been applied to the best approximation and … Read more