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.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. List of figures - p. ix 7. List of tables - p. xiii 8. Preface - p. xv 9. Acknowledgments - p. xvii 10. 1: Theoretical background - p. 1 11. 2: Nonexpansive mappings - p. 17 12. 3: Generalized nonexpansive mappings - p. 37 13. 4: Variational inequality - p. 69 14. 5: Minimization problems - p. 95 15. 6: Split feasibility problems - p. 133 16. 7: Variational inclusion problems - p. 153 17. 8: Equilibrium problems - p. 171 18. 9: Applications - p. 193 19. Index - p. 221
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.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. List of figures - p. ix 7. List of tables - p. xiii 8. Preface - p. xv 9. Acknowledgments - p. xvii 10. 1: Theoretical background - p. 1 11. 2: Nonexpansive mappings - p. 17 12. 3: Generalized nonexpansive mappings - p. 37 13. 4: Variational inequality - p. 69 14. 5: Minimization problems - p. 95 15. 6: Split feasibility problems - p. 133 16. 7: Variational inclusion problems - p. 153 17. 8: Equilibrium problems - p. 171 18. 9: Applications - p. 193 19. Index - p. 221
