Algorithms For Solving Common Fixed Point Problems

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Algorithms for Solving Common Fixed Point Problems

Author : Alexander J. Zaslavski
Publisher : Springer
ISBN 13 : 3319774379
Total Pages : 320 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Algorithms for Solving Common Fixed Point Problems by : Alexander J. Zaslavski

Download or read book Algorithms for Solving Common Fixed Point Problems written by Alexander J. Zaslavski and published by Springer. This book was released on 2018-05-02 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details approximate solutions to common fixed point problems and convex feasibility problems in the presence of perturbations. Convex feasibility problems search for a common point of a finite collection of subsets in a Hilbert space; common fixed point problems pursue a common fixed point of a finite collection of self-mappings in a Hilbert space. A variety of algorithms are considered in this book for solving both types of problems, the study of which has fueled a rapidly growing area of research. This monograph is timely and highlights the numerous applications to engineering, computed tomography, and radiation therapy planning. Totaling eight chapters, this book begins with an introduction to foundational material and moves on to examine iterative methods in metric spaces. The dynamic string-averaging methods for common fixed point problems in normed space are analyzed in Chapter 3. Dynamic string methods, for common fixed point problems in a metric space are introduced and discussed in Chapter 4. Chapter 5 is devoted to the convergence of an abstract version of the algorithm which has been called component-averaged row projections (CARP). Chapter 6 studies a proximal algorithm for finding a common zero of a family of maximal monotone operators. Chapter 7 extends the results of Chapter 6 for a dynamic string-averaging version of the proximal algorithm. In Chapters 8 subgradient projections algorithms for convex feasibility problems are examined for infinite dimensional Hilbert spaces.

Approximate Solutions of Common Fixed-Point Problems

Author : Alexander J. Zaslavski
Publisher : Springer
ISBN 13 : 3319332554
Total Pages : 457 pages
Book Rating : 4.3/5 (193 download)

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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 and published by Springer. This book was released on 2016-06-30 with total page 457 pages. 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

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Author : Heinz H. Bauschke
Publisher : Springer Science & Business Media
ISBN 13 : 1441995692
Total Pages : 409 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Fixed-Point Algorithms for Inverse Problems in Science and Engineering by : Heinz H. Bauschke

Download or read book Fixed-Point Algorithms for Inverse Problems in Science and Engineering written by Heinz H. Bauschke and published by Springer Science & Business Media. This book was released on 2011-05-27 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.

Solutions of Fixed Point Problems with Computational Errors

Author : Alexander J. Zaslavski
Publisher : Springer Nature
ISBN 13 : 3031508793
Total Pages : 392 pages
Book Rating : 4.0/5 (315 download)

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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 and published by Springer Nature. This book was released on with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Optimization on Solution Sets of Common Fixed Point Problems

Author : Alexander J. Zaslavski
Publisher : Springer Nature
ISBN 13 : 3030788490
Total Pages : 434 pages
Book Rating : 4.0/5 (37 download)

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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 and published by Springer Nature. This book was released on 2021-08-09 with total page 434 pages. 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.

Solutions of Fixed Point Problems with Computational Errors

Author : Aleksandr J. Zaslavskij
Publisher :
ISBN 13 : 9783031508806
Total Pages : 0 pages
Book Rating : 4.5/5 (88 download)

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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 and published by . This book was released on 2024 with total page 0 pages. 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.

Fixed Point Theory and Applications

Author : Ravi P. Agarwal
Publisher : Cambridge University Press
ISBN 13 : 1139433792
Total Pages : 182 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Fixed Point Theory and Applications by : Ravi P. Agarwal

Download or read book Fixed Point Theory and Applications written by Ravi P. Agarwal and published by Cambridge University Press. This book was released on 2001-03-22 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.

Fixed Points

Author : Stepan Karamardian
Publisher : Academic Press
ISBN 13 : 1483261131
Total Pages : 505 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Fixed Points by : Stepan Karamardian

Download or read book Fixed Points written by Stepan Karamardian and published by Academic Press. This book was released on 2014-05-10 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fixed Points: Algorithms and Applications covers the proceedings of the First International Conference on Computing Fixed Points with Applications, held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina on June 26-28, 1974. This book is composed of 21 chapters and starts with reviews of finding roots of polynomials by pivoting procedures and the relations between convergence and labeling in approximation algorithm. The next chapters deal with the principles of complementary pivot theory and the Markovian decision chains; the method of continuation for Brouwer fixed point calculation; a fixed point approach to stability in cooperative games; and computation of fixed points in a nonconvex region. Other chapters discuss a computational comparison of fixed point algorithms, the fundamentals of union jack triangulations, and some aspects of Mann’s iterative method for approximating fixed points. The final chapters consider the application of fixed point algorithms to the analysis of tax policies and the pricing for congestion in telephone networks. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.

Topics in Metric Fixed Point Theory

Author : Kazimierz Goebel
Publisher : Cambridge University Press
ISBN 13 : 9780521382892
Total Pages : 258 pages
Book Rating : 4.3/5 (828 download)

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Book Synopsis Topics in Metric Fixed Point Theory by : Kazimierz Goebel

Download or read book Topics in Metric Fixed Point Theory written by Kazimierz Goebel and published by Cambridge University Press. This book was released on 1990 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metric Fixed Point Theory has proved a flourishing area of research for many mathematicians. This book aims to offer the mathematical community an accessible, self-contained account which can be used as an introduction to the subject and its development. It will be understandable to a wide audience, including non-specialists, and provide a source of examples, references and new approaches for those currently working in the subject.

Advances in Metric Fixed Point Theory and Applications

Author : Yeol Je Cho
Publisher : Springer Nature
ISBN 13 : 9813366478
Total Pages : 503 pages
Book Rating : 4.8/5 (133 download)

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Book Synopsis Advances in Metric Fixed Point Theory and Applications by : Yeol Je Cho

Download or read book Advances in Metric Fixed Point Theory and Applications written by Yeol Je Cho and published by Springer Nature. This book was released on 2021-06-05 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects papers on major topics in fixed point theory and its applications. Each chapter is accompanied by basic notions, mathematical preliminaries and proofs of the main results. The book discusses common fixed point theory, convergence theorems, split variational inclusion problems and fixed point problems for asymptotically nonexpansive semigroups; fixed point property and almost fixed point property in digital spaces, nonexpansive semigroups over CAT(κ) spaces, measures of noncompactness, integral equations, the study of fixed points that are zeros of a given function, best proximity point theory, monotone mappings in modular function spaces, fuzzy contractive mappings, ordered hyperbolic metric spaces, generalized contractions in b-metric spaces, multi-tupled fixed points, functional equations in dynamic programming and Picard operators. This book addresses the mathematical community working with methods and tools of nonlinear analysis. It also serves as a reference, source for examples and new approaches associated with fixed point theory and its applications for a wide audience including graduate students and researchers.

Advances in Swarm Intelligence

Author : Ying Tan
Publisher : Springer Nature
ISBN 13 : 3031096770
Total Pages : 553 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Advances in Swarm Intelligence by : Ying Tan

Download or read book Advances in Swarm Intelligence written by Ying Tan and published by Springer Nature. This book was released on 2022-06-25 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set LNCS 13344 and 13345 constitutes the proceedings of the 13th International Conference on Advances in Swarm Intelligence, ICSI 2022, which took place in Xi’an, China, in July 2022. The theme of this year’s conference was “Serving Life with Swarm Intelligence”. The 85 full papers presented were carefully reviewed and selected from 171 submissions. The papers of the first part cover topics such as: Swarm Intelligence and Nature-Inspired Computing; Swarm-based Computing Algorithms for Optimization; Particle Swarm Optimization; Ant Colony Optimization; Differential Evolution; Genetic Algorithm and Evolutionary Computation; Fireworks Algorithms; Brain Storm Optimization Algorithm; Bacterial Foraging Optimization Algorithm; DNA Computing Methods; Multi-Objective Optimization; Swarm Robotics and Multi-Agent System; UAV Cooperation and Control; Machine Learning; Data Mining; and Other Applications.

Fixed Point Theory and Graph Theory

Author : Monther Alfuraidan
Publisher : Academic Press
ISBN 13 : 0128043652
Total Pages : 444 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Fixed Point Theory and Graph Theory by : Monther Alfuraidan

Download or read book Fixed Point Theory and Graph Theory written by Monther Alfuraidan and published by Academic Press. This book was released on 2016-06-20 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges. This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains. The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets. Introduces both metric fixed point and graph theory in terms of their disparate foundations and common application environments Provides a unique integration of otherwise disparate domains that aids both students seeking to understand either area and researchers interested in establishing an integrated research approach Emphasizes solution methods for fixed points in non-linear problems such as variational inequalities, split feasibility, and hierarchical variational inequality problems that is particularly appropriate for engineering and core science applications

Fixed Point Theory, Variational Analysis, and Optimization

Author : Saleh Abdullah R. Al-Mezel
Publisher : CRC Press
ISBN 13 : 1482222078
Total Pages : 370 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Fixed Point Theory, Variational Analysis, and Optimization by : Saleh Abdullah R. Al-Mezel

Download or read book Fixed Point Theory, Variational Analysis, and Optimization written by Saleh Abdullah R. Al-Mezel and published by CRC Press. This book was released on 2014-06-03 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fixed Point Theory, Variational Analysis, and Optimization not only covers three vital branches of nonlinear analysis—fixed point theory, variational inequalities, and vector optimization—but also explains the connections between them, enabling the study of a general form of variational inequality problems related to the optimality conditions involving differentiable or directionally differentiable functions. This essential reference supplies both an introduction to the field and a guideline to the literature, progressing from basic concepts to the latest developments. Packed with detailed proofs and bibliographies for further reading, the text: Examines Mann-type iterations for nonlinear mappings on some classes of a metric space Outlines recent research in fixed point theory in modular function spaces Discusses key results on the existence of continuous approximations and selections for set-valued maps with an emphasis on the nonconvex case Contains definitions, properties, and characterizations of convex, quasiconvex, and pseudoconvex functions, and of their strict counterparts Discusses variational inequalities and variational-like inequalities and their applications Gives an introduction to multi-objective optimization and optimality conditions Explores multi-objective combinatorial optimization (MOCO) problems, or integer programs with multiple objectives Fixed Point Theory, Variational Analysis, and Optimization is a beneficial resource for the research and study of nonlinear analysis, optimization theory, variational inequalities, and mathematical economics. It provides fundamental knowledge of directional derivatives and monotonicity required in understanding and solving variational inequality problems.

Mathematical Analysis and Applications

Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414342
Total Pages : 764 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-05-11 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Optimization Methods, Theory and Applications

Author : Honglei Xu
Publisher : Springer
ISBN 13 : 3662470446
Total Pages : 212 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Optimization Methods, Theory and Applications by : Honglei Xu

Download or read book Optimization Methods, Theory and Applications written by Honglei Xu and published by Springer. This book was released on 2015-06-17 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest research findings and state-of-the-art solutions on optimization techniques and provides new research direction and developments. Both the theoretical and practical aspects of the book will be much beneficial to experts and students in optimization and operation research community. It selects high quality papers from The International Conference on Optimization: Techniques and Applications (ICOTA2013). The conference is an official conference series of POP (The Pacific Optimization Research Activity Group; there are over 500 active members). These state-of-the-art works in this book authored by recognized experts will make contributions to the development of optimization with its applications.

Introduction to Hilbert Spaces with Applications

Author : Lokenath Debnath
Publisher : Elsevier
ISBN 13 : 0080455921
Total Pages : 599 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Introduction to Hilbert Spaces with Applications by : Lokenath Debnath

Download or read book Introduction to Hilbert Spaces with Applications written by Lokenath Debnath and published by Elsevier. This book was released on 2005-09-29 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory. Updated chapter on wavelets Improved presentation on results and proof Revised examples and updated applications Completely updated list of references

Metric Fixed Point Theory

Author : Pradip Debnath
Publisher : Springer Nature
ISBN 13 : 9811648964
Total Pages : 356 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Metric Fixed Point Theory by : Pradip Debnath

Download or read book Metric Fixed Point Theory written by Pradip Debnath and published by Springer Nature. This book was released on 2022-01-04 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects chapters on contemporary topics on metric fixed point theory and its applications in science, engineering, fractals, and behavioral sciences. Chapters contributed by renowned researchers from across the world, this book includes several useful tools and techniques for the development of skills and expertise in the area. The book presents the study of common fixed points in a generalized metric space and fixed point results with applications in various modular metric spaces. New insight into parametric metric spaces as well as study of variational inequalities and variational control problems have been included.