Optimization : Insights and Applications
Jan. Brinkhuis
Bok Engelsk 2011 · Electronic books.
| Annen tittel | |
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| Utgitt | Princeton : : Princeton University Press, , 2011.
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| Omfang | 1 online resource (683 p.)
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| Opplysninger | Description based upon print version of record.. - Cover; Title; Copyright; Contents; Preface; 0.1 Optimization: insights and applications; 0.2 Lunch, dinner, and dessert; 0.3 For whom is this book meant?; 0.4 What is in this book?; 0.5 Special features; Necessary Conditions: What Is the Point?; Chapter 1. Fermat: One Variable without Constraints; 1.0 Summary; 1.1 Introduction; 1.2 The derivative for one variable; 1.3 Main result: Fermat theorem for one variable; 1.4 Applications to concrete problems; 1.5 Discussion and comments; 1.6 Exercises; Chapter 2. Fermat: Two or More Variables without Constraints; 2.0 Summary; 2.1 Introduction. - 10.4 Proof of the necessary conditions. - 2.2 The derivative for two or more variables2.3 Main result: Fermat theorem for two or more variables; 2.4 Applications to concrete problems; 2.5 Discussion and comments; 2.6 Exercises; Chapter 3. Lagrange: Equality Constraints; 3.0 Summary; 3.1 Introduction; 3.2 Main result: Lagrange multiplier rule; 3.3 Applications to concrete problem; 3.4 Proof of the Lagrange multiplier rule; 3.5 Discussion and comments; 3.6 Exercise; Chapter 4. Inequality Constraints and Convexity; 4.0 Summary; 4.1 Introduction; 4.2 Main result: Karush-Kuhn-Tucker theorem; 4.3 Applications to concrete problem. - 4.4 Proof of the Karush-Kuhn-Tucker theorem4.5 Discussion and comments; 4.6 Exercises; Chapter 5. Second Order Conditions; 5.0 Summary; 5.1 Introduction; 5.2 Main result: second order conditions; 5.3 Applications to concrete problems; 5.4 Discussion and comments; 5.5 Exercises; Chapter 6. Basic Algorithms; 6.0 Summary; 6.1 Introduction; 6.2 Nonlinear optimization is difficult; 6.3 Main methods of linear optimization; 6.4 Line search; 6.5 Direction of descent; 6.6 Quality of approximation; 6.7 Center of gravity method; 6.8 Ellipsoid method; 6.9 Interior point methods. - 8.10 The best lunch and the second welfare theoremChapter 9. Mathematical Applications; 9.1 Fun and the quest for the essence; 9.2 Optimization approach to matrices; 9.3 How to prove results on linear inequalities; 9.4 The problem of Apollonius; 9.5 Minimization of a quadratic function: Sylvester's criterion and Gram's formula; 9.6 Polynomials of least deviation; 9.7 Bernstein inequality; Chapter 10. Mixed Smooth-Convex Problems; 10.1 Introduction; 10.2 Constraints given by inclusion in a cone; 10.3 Main result: necessary conditions for mixed smooth-convex problems. - Chapter 7. Advanced Algorithms7.1 Introduction; 7.2 Conjugate gradient method; 7.3 Self-concordant barrier methods; Chapter 8. Economic Applications; 8.1 Why you should not sell your house to the highest bidder; 8.2 Optimal speed of ships and the cube law; 8.3 Optimal discounts on airline tickets with a Saturday stayover; 8.4 Prediction of flows of cargo; 8.5 Nash bargaining; 8.6 Arbitrage-free bounds for prices; 8.7 Fair price for options: formula of Black and Scholes; 8.8 Absence of arbitrage and existence of a martingale; 8.9 How to take a penalty kick, and the minimax theorem. - 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 s
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| Emner | |
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| Dewey | |
| ISBN | 0691102872. - 9780691102870
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