This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant.

Beginning with an introduction, this monograph moves on to study:

· dynamic string-averaging methods for common fixed point problems in a Hilbert space

· dynamic string methods for common fixed point problems in a metric space· common fixed point problems in the spaces with distances of the Bregman type

· a proximal algorithm for finding a common zero of a family of maximal monotone operators

· subgradient projections algorithms for convex feasibility problems in Hilbert spaces

Studies the approximate solutions of common fixed point problems and convex feasibility problems in the presence of computational errors Examines the convergence of component-averaged row projections [CARP] Extends results for a dynamic string-averaging version of the proximal algorithm Includes supplementary material: sn.pub/extras

Autorentext

Alexander J. Zaslavski is professor in the Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel. He has authored numerous books with Springer, the most recent of which include Turnpike Theory for the Robinson-Solow-Srinivasan Model (978-3-030-60306-9), The Projected Subgradient Algorithm in Convex Optimization (978-3-030-60299-4), Convex Optimization with Computational Errors (978-3-030-37821-9), Turnpike Conditions in Infinite Dimensional Optimal Control (978-3-030-20177-7), Optimization on Solution Sets of Common Fixed Point Problems (978-3-030-78848-3).

Inhalt

1.Introduction.- 2. Dynamic string-averaging methods in Hilbert spaces.- 3. Iterative methods in metric spaces.- 4. Dynamic string-averaging methods in normed spaces.- 5. Dynamic string-maximum methods in metric spaces.- 6. Spaces with generalized distances.- 7. Abstract version of CARP algorithm.- 8. Proximal point algorithm.- 9. Dynamic string-averaging proximal point algorithm.- 10. Convex feasibility problems.- 11. Iterative subgradient projection algorithm.- 12. Dynamic string-averaging subgradient projection algorithm. References. Index.