A First Course in Optimization Theory

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.

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

About the Author

Rangarajan K. “Raghu” Sundaram is an Indian-born American academic. He is the Dean of the New York University Stern School of Business, and the author or co-author of two books.