A First Course in Optimization Theory

by Rangarajan K. Sundaram

Overview

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.

Product Details

ISBN-13:	9780521497190
Publisher:	Cambridge University Press
Publication date:	06/13/1996
Pages:	376
Product dimensions:	7.01(w) x 10.00(h) x 0.87(d)

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.

Editorial Reviews

'… the book is an excellent reference for self-studies, especially for students in business and economics.' H. Noltemeier, Würzberg

From the Publisher