Fixed Point Optimization Algorithms and Their Applications

by Watcharaporn Cholamjiak Ph.D.

Overview

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. - 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

Product Details

ISBN-13:	9780443335877
Publisher:	Morgan Kaufmann Publishers
Publication date:	11/23/2024
Series:	Advanced Studies in Complex Systems
Sold by:	Barnes & Noble
Format:	eBook
Pages:	200
File size:	40 MB
Note:	This product may take a few minutes to download.

About the Author

Dr. Watcharaporn Cholamjiak serves as an Associate Professor of Mathematics at the University of Phayao's School of Science in Thailand. She earned both her MSc and PhD in Mathematics from Chiang Mai University, under the guidance of Professor Suthep Suantai. Dr. Cholamjiak has an established collaboration with Professor Yeal Je Cho at Gyeongsang National University in Chinju, Korea, and has published numerous papers in highly regarded international journals. Her research has recently pivoted to the development of optimization algorithms for image restoration and signal recovery, areas in which she has produced significant published work. She is also a dedicated staff member of the Unit of Excellence in Image Recovery and Analysis and currently leads the Unit of Excellence in Data Analytics at the University of Phayao, focusing her research on the application of optimization algorithms in machine learning.
Dr. Watcharaporn Cholamjiak serves as an Associate Professor of Mathematics at the University of Phayao’s School of Science in Thailand. She earned both her MSc and PhD in Mathematics from Chiang Mai University, under the guidance of Professor Suthep Suantai. Dr. Cholamjiak has an established collaboration with Professor Yeal Je Cho at Gyeongsang National University in Chinju, Korea, and has published numerous papers in highly regarded international journals. Her research has recently pivoted to the development of optimization algorithms for image restoration and signal recovery, areas in which she has produced significant published work. She is also a dedicated staff member of the Unit of Excellence in Image Recovery and Analysis and currently leads the Unit of Excellence in Data Analytics at the University of Phayao, focusing her research on the application of optimization algorithms in machine learning.

Table of Contents

1. Theoretical Background2. Nonexpansive Mapping3. Generalized Nonexpansive Mapping4. Variational Inequality Problems5. Minimization Problems6. Split Feasibility Problems7. Variational Inclusion Problems8. Equilibrium Problems9. Applications