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
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
