Optimization : Insights and Applications

Jan Brinkhuis, Vladimir M. Tikhomirov - Collection Princeton Series in Applied Mathematics

658 pages, parution le 02/11/2005

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Résumé

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.

L'auteur - Jan Brinkhuis

Jan Brinkhuis is Associate Professor of Finance and Mathematical Methods and Techniques at the Econometric Institute of Erasmus University, Rotterdam.

L'auteur - Vladimir M. Tikhomirov

Vladimir Tikhomirov holds the Chair of Optimal Control in the Department of Mechanics and Mathematics at the Lomonosov Moscow State University.

Sommaire

Preface
Fermat: One Variable without Constraints
Fermat: Two or More Variables without Constraints
Lagrange: Equality Constraints
Inequality Constraints and Convexity
Second Order Conditions
Basic Algorithms
Advanced Algorithms
Economic Applications
Mathematical Applications
Mixed Smooth-Convex Problems
Dynamic Programming in Discrete Time
Dynamic Optimization in Continuous Time
Appendix A: On Linear Algebra: 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 E: Crash Course on Optimization Theory: Geometrical Style
Appendix F: Crash Course on Optimization Theory: Analytical Style
Appendix G: Conditions of Extremum from Fermat to Pontryagin
Appendix H: Solutions of Exercises of Chapters
Bibliography
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	Jan Brinkhuis, Vladimir M. Tikhomirov
Collection	Princeton Series in Applied Mathematics
Parution	02/11/2005
Nb. de pages	658
Format	16 x 24
Couverture	Relié
Poids	1086g
Intérieur	Noir et Blanc
EAN13	9780691102870
ISBN13	978-0-691-10287-0