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Author : Alexander J. Zaslavski
Release :
Genre :
Kind : eBook
Book Rating : 793/5 ( reviews)
Book Synopsis Solutions of Fixed Point Problems with Computational Errors by : Alexander J. Zaslavski
Download or read book Solutions of Fixed Point Problems with Computational Errors written by Alexander J. Zaslavski. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:
Author : Aleksandr J. Zaslavskij
Release : 2024
Genre : Mathematical optimization
Kind : eBook
Book Rating : 813/5 ( reviews)
Book Synopsis Solutions of Fixed Point Problems with Computational Errors by : Aleksandr J. Zaslavskij
Download or read book Solutions of Fixed Point Problems with Computational Errors written by Aleksandr J. Zaslavskij. This book was released on 2024. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the study of approximate solutions of fixed point problems in the presence of computational errors. It begins with a study of approximate solutions of star-shaped feasibility problems in the presence of perturbations. The goal is to show the convergence of algorithms, which are known as important tools for solving convex feasibility problems and common fixed point problems. The text also presents studies of algorithms based on unions of nonexpansive maps, inconsistent convex feasibility problems, and split common fixed point problems. A number of algorithms are considered for solving convex feasibility problems and common fixed point problems. The book will be of interest for researchers and engineers working in optimization, numerical analysis, and fixed point theory. It also can be useful in preparation courses for graduate students. The main feature of the book which appeals specifically to this audience is the study of the influence of computational errors for several important algorithms used for nonconvex feasibility problems.
Author : Alexander J. Zaslavski
Release : 2016-06-30
Genre : Mathematics
Kind : eBook
Book Rating : 554/5 ( reviews)
Book Synopsis Approximate Solutions of Common Fixed-Point Problems by : Alexander J. Zaslavski
Download or read book Approximate Solutions of Common Fixed-Point Problems written by Alexander J. Zaslavski. This book was released on 2016-06-30. Available in PDF, EPUB and Kindle. Book excerpt: 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“/p> · dynamic string-averaging version of the proximal algorithm · common fixed point problems in metric spaces · 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
Author : Alexander J. Zaslavski
Release : 2021
Genre :
Kind : eBook
Book Rating : 506/5 ( reviews)
Book Synopsis Optimization on Solution Sets of Common Fixed Point Problems by : Alexander J. Zaslavski
Download or read book Optimization on Solution Sets of Common Fixed Point Problems written by Alexander J. Zaslavski. This book was released on 2021. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a detailed study of the subgradient projection method and its variants for convex optimization problems over the solution sets of common fixed point problems and convex feasibility problems. These optimization problems are investigated to determine good solutions obtained by different versions of the subgradient projection algorithm in the presence of sufficiently small computational errors. The use of selected algorithms is highlighted including the Cimmino type subgradient, the iterative subgradient, and the dynamic string-averaging subgradient. All results presented are new. Optimization problems where the underlying constraints are the solution sets of other problems, frequently occur in applied mathematics. The reader should not miss the section in Chapter 1 which considers some examples arising in the real world applications. The problems discussed have an important impact in optimization theory as well. The book will be useful for researches interested in the optimization theory and its applications.
Author : Stephen M. Robinson
Release : 2014-05-10
Genre : Mathematics
Kind : eBook
Book Rating : 028/5 ( reviews)
Book Synopsis Analysis and Computation of Fixed Points by : Stephen M. Robinson
Download or read book Analysis and Computation of Fixed Points written by Stephen M. Robinson. This book was released on 2014-05-10. Available in PDF, EPUB and Kindle. Book excerpt: Analysis and Computation of Fixed Points contains the proceedings of a Symposium on Analysis and Computation of Fixed Points, held at the University of Wisconsin-Madison on May 7-8, 1979. The papers focus on the analysis and computation of fixed points and cover topics ranging from paths generated by fixed point algorithms to strongly stable stationary solutions in nonlinear programs. A simple reliable numerical algorithm for following homotopy paths is also presented. Comprised of nine chapters, this book begins by describing the techniques of numerical linear algebra that possess attractive stability properties and exploit sparsity, and their application to the linear systems that arise in algorithms that solve equations by constructing piecewise-linear homotopies. The reader is then introduced to two triangulations for homotopy fixed point algorithms with an arbitrary grid refinement, followed by a discussion on some generic properties of paths generated by fixed point algorithms. Subsequent chapters deal with topological perturbations in the numerical study of nonlinear eigenvalue and bifurcation problems; general equilibrium analysis of taxation policy; and solving urban general equilibrium models by fixed point methods. The book concludes with an evaluation of economic equilibrium under deformation of the economy. This monograph should be of interest to students and specialists in the field of mathematics.
