Fixed Point Theory, Variational Analysis, and Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed Point Theory, Variational Analysis, and Optimization write by Saleh Abdullah R. Al-Mezel. This book was released on 2014-06-03. Fixed Point Theory, Variational Analysis, and Optimization available in PDF, EPUB and Kindle. 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.
Fixed Point Theory, Variational Analysis, and Optimization
Fixed Point Theory, Variational Analysis, and Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed Point Theory, Variational Analysis, and Optimization write by Saleh Abdullah R. Al-Mezel. This book was released on 2014-01-01. Fixed Point Theory, Variational Analysis, and Optimization available in PDF, EPUB and Kindle. 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."
Fixed Point Theory and Graph Theory
Fixed Point Theory and Graph Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed Point Theory and Graph Theory write by Monther Alfuraidan. This book was released on 2016-06-20. Fixed Point Theory and Graph Theory available in PDF, EPUB and Kindle. 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 Algorithms for Inverse Problems in Science and Engineering
Fixed-Point Algorithms for Inverse Problems in Science and Engineering - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed-Point Algorithms for Inverse Problems in Science and Engineering write by Heinz H. Bauschke. This book was released on 2011-05-27. Fixed-Point Algorithms for Inverse Problems in Science and Engineering available in PDF, EPUB and Kindle. "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.
Variational Methods in Nonlinear Analysis
Variational Methods in Nonlinear Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Variational Methods in Nonlinear Analysis write by Dimitrios C. Kravvaritis. This book was released on 2020-04-06. Variational Methods in Nonlinear Analysis available in PDF, EPUB and Kindle. This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.
