Equilibrium Problems and Applications develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolved in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics.
This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis.
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. Dedication - p. v 6. About the Authors - p. xiii 7. Preface - p. xv 8. Acknowledgments - p. xix 9. Chapter 1: Preliminaries and Basic Mathematical Tools - p. xx 10. Chapter 2: An Overview on Equilibrium Problems - p. 16 11. Chapter 3: Mathematical Tools for Solving Equilibrium Problems - p. 33 12. Chapter 4: Existence of Solutions of Equilibrium Problems - p. 55 13. Chapter 5: Well-Posedness for the Equilibrium Problems - p. 127 14. Chapter 6: Variational Principles and Variational Analysis for the Equilibrium Problems - p. 150 15. Chapter 7: Applications to Sensitivity of Parametric Equilibrium Problems - p. 186 16. Chapter 8: Applications to Nash Equilibrium - p. 214 17. Chapter 9: Applications to Mathematical Economics - p. 259 18. Chapter 10: Applications to Variational Inequalities and Related Topics - p. 275 19. Chapter 11: Regularization and Numerical Methods for Equilibrium Problems - p. 321 20. Appendix A: Ekeland Variational Principle - p. 378 21. Appendix B: Minimization Problems and Fixed Point Theorems - p. 385 22. Appendix C: Nonsmooth Clarke Theory and Generalized Derivatives - p. 393 23. Appendix D: Elements of Szulkin Critical Point Theory - p. 398 24. Bibliography - p. 403 25. Index - p. 411
Equilibrium Problems and Applications develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolved in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics.
This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis.
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. Dedication - p. v 6. About the Authors - p. xiii 7. Preface - p. xv 8. Acknowledgments - p. xix 9. Chapter 1: Preliminaries and Basic Mathematical Tools - p. xx 10. Chapter 2: An Overview on Equilibrium Problems - p. 16 11. Chapter 3: Mathematical Tools for Solving Equilibrium Problems - p. 33 12. Chapter 4: Existence of Solutions of Equilibrium Problems - p. 55 13. Chapter 5: Well-Posedness for the Equilibrium Problems - p. 127 14. Chapter 6: Variational Principles and Variational Analysis for the Equilibrium Problems - p. 150 15. Chapter 7: Applications to Sensitivity of Parametric Equilibrium Problems - p. 186 16. Chapter 8: Applications to Nash Equilibrium - p. 214 17. Chapter 9: Applications to Mathematical Economics - p. 259 18. Chapter 10: Applications to Variational Inequalities and Related Topics - p. 275 19. Chapter 11: Regularization and Numerical Methods for Equilibrium Problems - p. 321 20. Appendix A: Ekeland Variational Principle - p. 378 21. Appendix B: Minimization Problems and Fixed Point Theorems - p. 385 22. Appendix C: Nonsmooth Clarke Theory and Generalized Derivatives - p. 393 23. Appendix D: Elements of Szulkin Critical Point Theory - p. 398 24. Bibliography - p. 403 25. Index - p. 411
