Optimization: Insights and Applications

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Princeton University Press, Feb 11, 2011 - Mathematics - 680 pages
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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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Contents

One Variable without Constraints
3
Two or More Variables without Constraints
85
Equality Constraints
135
Chapter 4 Inequality Constraints and Convexity
199
Chapter 5 Second Order Conditions
261
Chapter 6 Basic Algorithms
273
Chapter 7 Advanced Algorithms
325
Chapter 8 Economic Applications
363
Vector and Matrix Calculus
503
Appendix B On Real Analysis
519
Appendix C The Weierstrass Theorem on Existence of Global Solutions
537
Appendix D Crash Course on Problem Solving
547
Geometrical Style
553
Analytical Style
561
Appendix G Conditions of Extremum from Fermat to Pontryagin
583
Appendix H Solutions of Exercises of Chapters 14
601

Chapter 9 Mathematical Applications
391
Chapter 10 Mixed SmoothConvex Problems
417
Chapter 11 Dynamic Programming in Discrete Time
441
Chapter 12 Dynamic Optimization in Continuous Time
475
Bibliography
645
Index
651
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About the author (2011)

Jan Brinkhuis is Associate Professor of Finance and Mathematical Methods and Techniques at the Econometric Institute of Erasmus University, Rotterdam. Vladimir Tikhomirov holds the Chair of Optimal Control in the Department of Mechanics and Mathematics at the Lomonosov Moscow State University.

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