Nonlinear optimization : models and applications /
Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is...
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| Format: | eBook |
| Language: | English |
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Boca Raton, FL :
Chapman and Hall/CRC,
2021.
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| Edition: | First edition. |
| Series: | Textbooks in mathematics (Boca Raton, Fla.)
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Chapter 1. Nonlinear Optimization Overview1.1 Introduction1.2 Modeling1.3 ExercisesChapter 2. Review of Single Variable Calculus Topics 2.1 Limits 2.2 Continuity 2.3 Differentiation 2.4 ConvexityChapter 3. Single Variable Optimization 3.1 Introduction 3.2 Optimization Applications 3.3 Optimization ModelsConstrained Optimization by CalculusChapter 4. Single Variable Search Methods4.1 Introduction 4.2 Unrestricted Search 4.3 Dichotomous Search 4.4 Golden Section Search 4.5 Fibonacci Search 4.6 Newton's Method 4.7 Bisection Derivative SearchChapter 5. Review of MV Calculus Topics5.1 Introduction, Basic Theory, and Partial Derivatives5.2 Directional Derivatives and The GradientChapter 6. MV Optimization 6.1 Introduction 6.2 The Hessian 6.3 Unconstrained OptimizationConvexity and The Hessian MatrixMax and Min Problems with Several VariablesChapter 7. Multi-variable Search Methods 7.1 Introduction7.2 Gradient Search7.3 Modified Newton's MethodChapter 8. Equality Constrained Optimization: Lagrange Multipliers 8.1 Introduction and Theory 8.2 Graphical Interpretation 8.3 Computational Methods 8.4 Modeling and ApplicationsChapter 9. Inequality Constrained Optimization; Kuhn-Tucker Methods 9.1 Introduction 9.2 Basic Theory 9.3 Graphical Interpretation and Computational Methods 9.4 Modeling and ApplicationsChapter 10. Method of Feasible Directions and Other Special NL Methods 10.1 Methods of Feasible DirectionsNumerical methods (Directional Searches)Starting Point Methods 10.2 Separable Programming 10.3 Quadratic ProgrammingChapter 11. Dynamic Programming 11.1 Introduction 11.2 Continuous Dynamic Programming 11.3 Modeling and Applications with Continuous DP 11.4 Discrete Dynamic Programming 11.5 Modeling and Applications with Discrete Dynamic Programming