Optimization: Insights and Applications
Princeton University Press, Feb 11, 2011 - Mathematics - 680 pages
This self-contained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization.
The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising.
A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the Fermat-Lagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant.
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Two or More Variables without Constraints
Chapter 4 Inequality Constraints and Convexity
Chapter 5 Second Order Conditions
Chapter 6 Basic Algorithms
Chapter 7 Advanced Algorithms
Chapter 8 Economic Applications
Vector and Matrix Calculus
Appendix B On Real Analysis
Appendix C The Weierstrass Theorem on Existence of Global Solutions
Appendix D Crash Course on Problem Solving
Appendix G Conditions of Extremum from Fermat to Pontryagin
Appendix H Solutions of Exercises of Chapters 14