A First Course in Optimization Theory
Cambridge University Press, 8/29/1996
EAN 9780521497701, ISBN10: 0521497701
Paperback, 376 pages, 25.4 x 17.5 x 2.2 cm
Language: English
Originally published in English
This book, first published in 1996, 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. Each chapter contains a number of detailed examples explaining both the theory and its applications for first-year master's and graduate students. 'Cookbook' procedures are accompanied by a discussion of when such methods are guaranteed to be successful, and, equally importantly, when they could fail. Each result in the main body of the text is also accompanied by a complete proof. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.
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.
'... the book is an excellent reference for self-studies, especially for students in business and economics.' H. Noltemeier, Würzberg