Fixed Point Optimization Algorithms and Their Applications
- 1st Edition - November 23, 2024
- Imprint: Morgan Kaufmann
- Author: Watcharaporn Cholamjiak
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 3 3 5 8 6 - 0
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 3 3 5 8 7 - 7
Fixed Point Optimization Algorithms and Their Applications discusses how the relationship between fixed point algorithms and optimization problems is connected and demonstrates ha… Read more
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Request a sales quoteFixed 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
Researchers in computational modelling, applied mathematicians, and computer scientists working with researchers, engineers, and scientists in a wide range of modelling applications for machine learning, engineering, and scientific research. The primary audience also includes researchers and professionals in the fields of mathematics, IT, physics, engineering, biomedicine, AI, ML, biology, and healthcare, where fixed point algorithms and optimization algorithms can be applied.
- Title of Book
- Cover image
- Title page
- Table of Contents
- Copyright
- List of figures
- List of tables
- Preface
- Acknowledgments
- 1: Theoretical background
- 1.1. Notations and definitions
- 1.2. Metric projection
- 1.3. Linear and adjoint operators
- 1.4. Essential lemmas and theorems
- 2: Nonexpansive mappings
- 2.1. Definitions and principle properties
- 2.2. Fixed point algorithms and convergence analysis
- 2.3. Practical guide to projection algorithms and their implementation
- 3: Generalized nonexpansive mappings
- 3.1. G-nonexpansive mappings
- 3.2. Multivalued mappings
- 3.2.1. Quasi-nonexpansive multivalued mappings
- 3.2.2. Hybrid multivalued mappings
- 4: Variational inequality
- 4.1. Nonexpansive mappings and fixed point equivalences
- 4.2. Algorithms for variational inequality
- 4.3. Examples and numerical results in infinite-dimensional spaces
- 5: Minimization problems
- 5.1. Differentiable function
- 5.1.1. Gradient function
- 5.1.2. Minimizing differentiable functions
- 5.2. Partial differentiable function
- 5.2.1. Proximal operator
- 5.2.2. Minimizing partial differentiable functions
- 5.3. Minimizing the sum of two functions
- 5.3.1. Convergence analysis tools
- 5.3.2. Convergence of algorithms
- 5.4. Examples and numerical results in infinite-dimensional spaces
- 6: Split feasibility problems
- 6.1. Definitions and lemmas
- 6.2. Algorithms and convergence theorems
- 6.3. Examples and numerical results in infinite-dimensional spaces
- 7: Variational inclusion problems
- 7.1. One monotone operator
- 7.2. Sum of two monotone operators
- 7.3. Examples and numerical results in infinite-dimensional spaces
- 8: Equilibrium problems
- 8.1. Equilibrium problems
- 8.2. Split equilibrium problems
- 8.3. Examples and numerical results in infinite-dimensional spaces
- 9: Applications
- 9.1. Inertial techniques
- 9.2. Signal recovery
- Model 1: regularized least squares
- Model 2: constrained least squares
- 9.3. Image restoration
- 9.4. Machine learning
- Index
- Edition: 1
- Published: November 23, 2024
- Imprint: Morgan Kaufmann
- No. of pages: 244
- Language: English
- Paperback ISBN: 9780443335860
- eBook ISBN: 9780443335877
WC
Watcharaporn Cholamjiak
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.
Affiliations and expertise
Associate Professor of Mathematics at the University of Phayao’s School of Science in Thailand.Read Fixed Point Optimization Algorithms and Their Applications on ScienceDirect