Chapter 2. Fermat: Two or More Variables without Constraints

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Preface xi
4. Necessary Conditions: What Is the Point? 1
5. Chapter 1. Fermat: One Variable without Constraints 3
6. Chapter 2. Fermat: Two or More Variables without Constraints 85
7. Chapter 3. Lagrange: Equality Constraints 135
8. Chapter 4. Inequality Constraints and Convexity 199
9. Chapter 5. Second Order Conditions 261
10. Chapter 6. Basic Algorithms 273
11. Chapter 7. Advanced Algorithms 325
12. Chapter 8. Economic Applications 363
13. Chapter 9. Mathematical Applications 391
14. Chapter 10. Mixed Smooth-Convex Problems 417
15. Chapter 11. Dynamic Programming in Discrete Time 441
16. Chapter 12. Dynamic Optimization in Continuous Time 475
17. Appendix A. On Linear Algebra: Vector and Matrix Calculus 503
18. Appendix B. On Real Analysis 519
19. Appendix C. The Weierstrass Theorem on Existence of Global Solutions 537
20. Appendix D. Crash Course on Problem Solving 547
21. Appendix E. Crash Course on Optimization Theory: Geometrical Style 553
22. Appendix F. Crash Course on Optimization Theory: Analytical Style 561
23. Appendix G. Conditions of Extremum from Fermat to Pontryagin 583
24. Appendix H. Solutions of Exercises of Chapters 1–4 601
25. Bibliography 645
26. Index 651