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E-raamat: Nonlinear Optimization: Models and Applications [Taylor & Francis e-raamat]

(U.S. Naval Post Graduate School)
  • Formaat: 394 pages, 49 Tables, black and white; 50 Illustrations, black and white
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 24-Dec-2020
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9781003009573
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  • Taylor & Francis e-raamat
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Nonlinear Optimization: Models and ApplicationsSuurem pilt
  • Formaat: 394 pages, 49 Tables, black and white; 50 Illustrations, black and white
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 24-Dec-2020
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9781003009573
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003009573
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 no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques).

Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB®, and Maple to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application.

Nonlinear Optimization: Models and Applications:











Emphasizes process and interpretation throughout





Presents a general classification of optimization problems





Addresses situations that lead to models illustrating many types of optimization problems





Emphasizes model formulations





Addresses a special class of problems that can be solved using only elementary calculus





Emphasizes model solution and model sensitivity analysis

About the author:

William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.
Preface: Nonlinear Optimization-Models and Applications xiii
Acknowledgments xix
Author xxi
1 Introduction to Optimization Models 1(34)
1.1 Introduction
1(3)
1.1.1 History
2(1)
1.1.2 Applications of Optimization
3(1)
1.1.3 Modeling
3(1)
1.2 Classifying Optimization Problems
4(4)
1.3 Review of Mathematical Programming with Excel Technology
8(17)
1.3.1 Excel Using the Solver
10(10)
1.3.2 Examples for Integer, Mixed-Integer, and Nonlinear Optimization
20(5)
1.4 Exercises
25(1)
1.5 Review of the Simplex Method in Excel Using Revised Simplex
26(7)
1.5.1 Steps of the Simplex Method
29(4)
References and Suggested Further Reading
33(2)
2 Review of Differential Calculus 35(16)
2.1 Limits
35(4)
2.2 Continuity
39(1)
2.3 Differentiation
40(3)
2.3.1 Increasing and Decreasing Functions
43(1)
2.3.2 Higher Derivatives
43(1)
2.4 Convex and Concave Functions
43(6)
Exercises
48(1)
References and Suggested Reading
49(2)
3 Single-Variable Unconstrained Optimization 51(20)
3.1 Introduction
51(1)
3.2 Single-Variable Optimization and Basic Theory
52(2)
3.3 Basic Applications of Max-Min Theory
54(5)
Exercises
57(2)
3.4 Applied Single-Variable Optimization Models
59(10)
Exercises
65(3)
Projects
68(1)
References and Suggested Reading
69(2)
4 Numerical Search Techniques in Single-Variable Optimization 71(32)
4.1 Single-Variable Techniques
71(20)
4.1.1 Unrestricted Search
73(1)
4.1.2 Exhaustive Search
74(1)
4.1.3 Dichotomous Search
74(2)
4.1.4 Golden Section Search
76(1)
4.1.5 Finding the Maximum of a Function over an Interval with Golden Section
77(2)
4.1.6 Golden Section Search with Technology
79(6)
4.1.6.1 Excel Golden Search
79(1)
4.1.6.2 Maple Golden Search
80(2)
4.1.6.3 MATLAB Golden Search
82(3)
4.1.7 Illustrious Examples with Technology
85(3)
4.1.8 Fibonacci's Search
88(3)
4.1.8.1 Finding the Maximum of a Function over an Interval with the Fibonacci Method
88(3)
4.2 Interpolation with Derivatives: Newton's Method
91(10)
4.2.1 Finding the Critical Points (Roots) of a Function
91(1)
4.2.2 The Basic Application
92(2)
4.2.3 Newton's Method to Find Critical Points with Technology
94(1)
4.2.4 Excel: Newton's Method
94(1)
4.2.5 Maple: Newton's Method
94(2)
4.2.6 Newton's Method for Critical Points with MATLAB
96(2)
4.2.7 The Bisection Method with Derivatives
98(2)
Exercises
100(1)
Projects
100(1)
References and Suggested Further Readings
101(2)
5 Review of Multivariable Differential Calculus 103(12)
5.1 Introduction: Basic Theory and Partial Differentiation
103(6)
5.2 Directional Derivatives and the Gradient
109(4)
Exercises
113(1)
References and Suggested Reading
114(1)
6 Models Using Unconstrained Optimization: Maximization and Minimization with Several Variables 115(28)
6.1 Introduction
115(2)
6.2 The Hessian Matrix
117(11)
6.3 Unconstrained Optimization
128(11)
Exercises
136(3)
6.4 Eigenvalues
139(2)
Exercises
140(1)
Reference and Further Suggested Reading
141(2)
7 Multivariate Optimization Search Techniques 143(30)
7.1 Introduction
143(1)
7.2 Gradient Search Methods
143(8)
7.3 Examples of Gradient Search
151(7)
7.4 Modified Newton's Method
158(8)
7.4.1 Modified Newton with Technology
162(4)
Exercises
166(1)
7.5 Comparisons of Methods
166(4)
7.5.1 Maple Code for Steepest Ascent Method (See Fox and Richardson)
166(2)
7.5.2 Newton's Method for Optimization in Maple
168(2)
Exercises
170(1)
Projects
Chapter 7
171(1)
References and Suggested Reading
171(2)
8 Optimization with Equality Constraints 173(22)
8.1 Introduction
173(1)
8.2 Equality Constraints Method of Lagrange Multipliers
173(1)
8.3 Introduction and Basic Theory
174(2)
8.4 Graphical Interpretation of Lagrange Multipliers
176(2)
8.5 Computational Method of Lagrange Multipliers
178(10)
Lagrange Method with Technology
180(8)
8.6 Applications with Lagrange Multipliers
188(6)
Exercises
191(2)
Projects
193(1)
References and Suggested Reading
194(1)
9 Inequality Constraints: Necessary/Sufficient Kuhn-Tucker Conditions (KTC) 195(36)
9.1 Introduction to KTC
195(1)
9.2 Basic Theory of Constrained Optimization
196(4)
9.2.1 Necessary and Sufficient Conditions
197(3)
9.3 Geometric Interpretation of KTC
200(4)
9.3.1 Spanning Cones (Optional)
200(4)
9.4 Computational KTC with Maple
204(14)
9.5 Modeling and Application with KTC
218(11)
Exercises
225(3)
Project
228(1)
Manufacturing
228(1)
References and Suggested Reading
229(2)
10 Specialized Nonlinear Optimization Methods 231(28)
10.1 Introduction
231(3)
10.1.1 Numerical and Heuristic Methods
231(3)
10.1.2 Technology
234(1)
10.2 Method of Feasible Directions
234(5)
Exercises
238(1)
10.3 Quadratic Programming
239(8)
Exercises
246(1)
10.4 Separable Programming
247(10)
10.4.1 Adjacency Assumptions
248(1)
10.4.2 Linearization Property
248(9)
Exercises
257(1)
References and Suggested Reading
257(2)
11 Dynamic Programming 259(20)
11.1 Introduction: Basic Concepts and Theory
259(3)
11.1.1 Characteristics of Dynamic Programming
261(1)
11.1.2 Working Backwards
261(1)
11.2 Continuous DP
262(2)
11.3 Modeling and Applications of Continuous DP
264(3)
Exercises
266(1)
11.4 Models of Discrete Dynamic Programming
267(3)
11.5 Modeling and Applications of Discrete DP
270(8)
Exercises
276(2)
References and Suggested Readings
278(1)
12 Data Analysis with Regression Models, Advanced Regression Models, and Machine Learning through Optimization 279(82)
12.1 Introduction and Machine Learning
279(3)
12.1.1 Machine Learning
280(2)
12.1.1.1 Data Cleaning and Breakdown
281(1)
12.1.1.2 Engineering
282(1)
12.1.1.3 Model Fitting
282(1)
12.2 The Different Curve Fitting Criterion
282(5)
12.2.1 Fitting Criterion 1: Least Squares
282(2)
12.2.2 Fitting Criterion 2: Minimize the Sum of the Absolute Deviations
284(1)
12.2.3 Fitting Criterion 3: Chebyshev's Criterion or Minimize the Largest Error
285(1)
Exercises
285(2)
12.3 Introduction to Simple Linear and Polynomial Regression
287(4)
12.3.1 Excel
288(1)
12.3.2 Regression in Maple
289(1)
12.3.3 MATLAB
290(1)
Exercises
291(1)
12.4 Diagnostics in Regression
291(5)
12.4.1 Example for the Common Sense Test
294(2)
12.4.1.1 Exponential Decay Example
294(2)
12.4.2 Multiple Linear Regression
296(1)
Exercises
296(1)
12.5 Nonlinear Regression through Optimization
296(26)
12.5.1 Exponential Regression
297(10)
12.5.1.1 Newton-Raphson Algorithm
298(9)
12.5.2 Sine Regression Using Optimization
307(5)
12.5.3 Illustrative Examples
312(10)
12.5.3.1 Nonlinear Regression (Exponential Decay)
312(10)
Exercises
322(1)
12.6 One-Predictor Logistic and One-Predictor Poisson Regression Models
322(37)
12.6.1 Logistic Regression and Poisson Regression with Technology
323(12)
12.6.1.1 Logistic Regression with Technology
323(7)
12.6.1.2 Simple Poisson Regression with Technology
330(5)
12.6.2 Logistic Regression Illustrious Examples
335(2)
12.6.3 Poisson Regression Discussion and Examples
337(6)
12.6.3.1 Normality Assumption Lost
338(4)
12.6.3.2 Estimates of Regression Coefficients
342(1)
12.6.4 Illustrative Poisson Regression Examples
343(11)
12.6.4.1 Maple
343(11)
Exercises
354(4)
Projects
358(1)
12.7 Conclusions and Summary
359(1)
References and Suggested Reading
359(2)
Answers to Selected Problems 361(28)
Index 389
Dr. William P. Fox is a professor in the Department of Defense Analysis at the Naval Postgraduate School and currently teaches a three course sequence in mathematical modeling for decision making. He received his Ph.D. at Clemson University. He has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics for eight years. He has many publications and scholarly activities including sixteen books, one hundred and fifty journal articles, and about one hundred and fifty conference presentations, and workshops. He was Past- President of the Military Application Society of INFORMS and is the current Vice Chair for Programs for BIG SIGMAA.
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