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Fixed Point Optimization Algorithms and Their Applications

2024-12-11 分类：Kindle Edition 评论(0)

Fixed Point Optimization Algorithms and Their Applications (Advanced Studies in Complex Systems)

Fixed Point Optimization Algorithms and Their Applications (Advanced Studies in Complex Systems)

Author:by Watcharaporn Cholamjiak Ph.D. (Author)

Publisher:‏Morgan Kaufmann

Edition:‏1st edition

Publication Date:‏2024-12-18

Language:English

Paperback:244pages

ISBN-10:0443335869

ISBN-13:9780443335860

Book Description

Fixed Point Optimization Algorithms and Their Applications discusses how the relationship between fixed point algorithms and optimization problems is connected and demonstrates hands-on applications of the algorithms in fields such as image restoration, signal recovery, and machine learning. The author presents algorithms for non-expansive and generalized non-expansive mappings in Hilbert space, and includes solutions to many optimization problems across a range of scientific research and real-world applications. From foundational concepts, the book proceeds to present a variety of optimization algorithms, including fixed point theories, convergence theorems, variational inequality problems, minimization problems, split feasibility problems, variational inclusion problems, and equilibrium problems.

This book will equip readers with the theoretical mathematics background and necessary tools to tackle challenging optimization problems involving a range of algebraic methods, empowering them to apply these techniques in their research, professional work, or academic pursuits.

  • Demonstrates how to create hybrid algorithms for many optimization problems with non-expansive mappings to solve real-world problems
  • Shows readers how to solve image restoration problems using optimization algorithms
  • Includes coverage of signal recovery problems using optimization algorithms
  • Shows readers how to solve data classification problems using optimization algorithms in machine learning with many types of datasets, such as those used in medicine, mathematics, computer science, and engineering

Review

A complete guide to the development of hybrid algorithms for optimization problems involving nonexpansive mappings and their applications

From the Back Cover

Fixed Point Optimization Algorithms and Their Applications discusses how the relationship between fixed point algorithms and optimization problems is connected and demonstrates hands-on applications of the algorithms in fields such as image restoration, signal recovery, and machine learning. The book is divided into nine chapters beginning with foundational concepts of normed linear spaces, Banach spaces, and Hilbert spaces, along with nonlinear operators and useful lemmas and theorems for proving the book’s main results. The author presents algorithms for nonexpansive and generalized nonexpansive mappings in Hilbert space, and presents solutions to many optimization problems across a range of scientific research and real-world applications. From foundational concepts, the book proceeds to present a variety of optimization algorithms, including fixed point theories, convergence theorems, variational inequality problems, minimization problems, split feasibility problems, variational inclusion problems, and equilibrium problems. Fixed Point Optimization Algorithms and Their Applications equips readers with the theoretical mathematics background and necessary tools to tackle challenging optimization problems involving a range of algebraic methods, empowering them to apply these techniques in their research, professional work, or academic pursuits.

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