A first course in optimization theory
- Cambridge Cambridge University Press 2011
- xvii, 357 p.
Table of Contents 1. Mathematical preliminaries 2. Optimization in Rn 3. Existence of solutions: the Weierstrass theorem 4. Unconstrained optima 5. Equality constraints and the theorem of Lagrange 6. Inequality constraints and the theorem of Kuhn and Tucker 7. Convex structures in optimization theory 8. Quasi-convexity and optimization 9. Parametric continuity: the maximum theorem 10. Supermodularity and parametric monotonicity 11. Finite-horizon dynamic programming 12. Stationary discounted dynamic programming Appendix A. Set theory and logic: an introduction Appendix B. The real line Appendix C. Structures on vector spaces Bibliography.
This book introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.