Optimization on Solution Sets of Common Fixed Point Problems - 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 Optimization on Solution Sets of Common Fixed Point Problems write by Alexander J. Zaslavski. This book was released on 2021. Optimization on Solution Sets of Common Fixed Point Problems available in PDF, EPUB and Kindle. 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.
Optimization on Solution Sets of Common Fixed Point Problems
Optimization on Solution Sets of Common Fixed Point Problems - 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 Optimization on Solution Sets of Common Fixed Point Problems write by Alexander J. Zaslavski. This book was released on 2021-08-09. Optimization on Solution Sets of Common Fixed Point Problems available in PDF, EPUB and Kindle. 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
Solutions of Fixed Point Problems with Computational Errors - 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 Solutions of Fixed Point Problems with Computational Errors write by Alexander J. Zaslavski. This book was released on . Solutions of Fixed Point Problems with Computational Errors available in PDF, EPUB and Kindle.
Approximate Solutions of Common Fixed-Point Problems
Approximate Solutions of Common Fixed-Point Problems - 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 Approximate Solutions of Common Fixed-Point Problems write by Alexander J. Zaslavski. This book was released on 2016-06-30. Approximate Solutions of Common Fixed-Point Problems available in PDF, EPUB and Kindle. 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 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 2014-06-03. 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.
