common fixed point problem – Optimization Online

Strong convergence, perturbation resilience and superiorization of Generalized Modular String-Averaging with infinitely many input operators

Published: 2026/03/16

We study the strong convergence and bounded perturbation resilience of iterative algorithms based on the Generalized Modular String-Averaging (GMSA) procedure for infinite sequences of input operators under a general admissible control. These methods address a variety of feasibility-seeking problems in real Hilbert spaces, including the common fixed point problem and the convex feasibility problem. In … Read more

General Perturbation Resilient Dynamic String-Averaging for Inconsistent Problems with Superiorization

Published: 2025/07/02

Kay Barshad

Yair Censor

Constrained Nonlinear Optimization, Convex Optimization Approximately shrinking operator, bounded perturbation resilience, bounded regularity, coherence, coherent sequence of operators, common fixed point problem, convex feasibility problem, dynamic string-averaging, Fej{\'e}r monotonicity, metric projection, nonexpansive operator, strong coherence, strongly coherent sequence of operators, superiorization, weak convergence, weak regularity.

In this paper we introduce a General Dynamic String-Averaging (GDSA) iterative scheme and investigate its convergence properties in the inconsistent case, that is, when the input operators don’t have a common fixed point. The Dynamic String-Averaging Projection (DSAP) algorithm itself was introduced in an 2013 paper, where its strong convergence and bounded perturbation resilience were … Read more

Concrete convergence rates for common fixed point problems under Karamata regularity

Published: 2024/07/18

Tianxiang Liu

Bruno F. Lourenço

Convex and Nonsmooth Optimization common fixed point problem, concrete rates, Karamata regularity, o-minimal structure, quasi-cyclic algorithm, regular variation and Karamata theory

We introduce the notion of Karamata regular operators, which is a notion of regularity that is suitable for obtaining concrete convergence rates for common fixed point problems. This provides a broad framework that includes, but goes beyond, Hölderian error bounds and Hölder regular operators. By concrete, we mean that the rates we obtain are explicitly … Read more

A generalized block-iterative projection method for the common fixed point problem induced by cutters

Published: 2022/04/22

Yair Censor

Daniel Reem

Maroun Zaknoon

Convex Optimization, Nonlinear Optimization block iterative projection (BIP), common fixed point problem, cutter, perturbation, weight function

The block-iterative projections (BIP) method of Aharoni and Censor [Block-iterative projection methods for parallel computation of solutions to convex feasibility problems, Linear Algebra and its Applications 120, (1989), 165-175] is an iterative process for finding asymptotically a point in the nonempty intersection of a family of closed convex subsets. It employs orthogonal projections onto the … Read more