Fixed Point Optimization Algorithms and Their Applications (Advanced Studies in Complex Systems)
Author: by Watcharaporn Cholamjiak Ph.D. (Author)
Publisher finelybook 出版社: Morgan Kaufmann
Edition 版次: 1st edition
Publication Date 出版日期: 2024-12-18
Language 语言: English
Print Length 页数: 244 pages
ISBN-10: 0443335869
ISBN-13: 9780443335860
Book Description
By finelybook
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.
About the Author
Dr. Watcharaporn Cholamjiak is currently working as an Associate Professor of Mathematics in the School of Science, University of Phayao, Thailand. She completed her MSc and PhD from Chiang Mai University, Thailand. Dr. Cholamjiak has been a collaborative researcher at Gyeongsang National University, Chinju, Korea
with Dr. Yeal Je Cho. Dr. Cholamjiak has published dozens of papers in internationally reputed Journals. Recently, she has been interested in applying optimization algorithms to solve image restoration and signal recovery and has published many papers on this topic. She is a staff member of the Unit of Excellence in image recovery and analysis at the University of Phayao. Her current research involves applying optimization algorithms to use in machine learning, and she is currently Department Head of the Unit of Excellence in Data Analytics at the University of Phayao.
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