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Tables of Contents for Optimization Concepts and Applications in Engineering
Chapter/Section Title
Page #
Page Count
Preface
x
Preliminary Concepts
1
20
Introduction
1
1
Historical Sketch
2
1
The Nonlinear Programming Problem
3
3
Mathematical Fundamentals
6
9
Conclusion
15
6
Problems
17
1
Computer Programs
17
4
One-Dimensional Unconstrained Minimization
21
35
Introduction
21
1
Single-Variable Minimization
21
7
Unimodality and Bracketing the Minimum
28
2
Fibonacci Method
30
6
Golden Section Method
36
3
Polynomial-Based Methods
39
4
Zero of a Function
43
3
Conclusion
46
10
Problems
47
4
Computer Programs
51
5
Unconstrained Minimization
56
36
Introduction
56
1
Necessary and Sufficient Conditions for Optimality
57
4
Convexity
61
2
Basic Concepts: Starting Design, Direction Vetor, and Step Size
63
1
The Steepest Descent Method
64
6
The Conjugate Gradient Method
70
4
Newton's Method
74
4
Quasi-Newton Methods
78
3
Trust Region Methods
81
11
Problems
83
3
Computer Programs
86
6
Linear Programming
92
49
Introduction
92
1
Linear Programming Problem
92
2
LP Problems Involving LE (≤) Constraints
94
2
The Simplex Method
96
4
Treatment of GE and EQ Constraints
100
5
The Two-Phase Approach
101
3
The Big M Method
104
1
Revised Simplex Method
105
3
Duality in Linear Programming
108
2
The Dual Simplex Method
110
3
Sensitivity Analysis
113
3
Interior Approach of Dikin
116
3
Problem Modeling
119
6
Quadratic Programming and the Linear Complementary Problem (LCP)
125
3
Conclusion
128
13
Problems
128
1
Computer Programs
128
13
Constrained Minimization
141
81
Introduction and Problem Formulation
141
3
Graphical Solution of Two-Variable Problems
144
2
Necessary Conditions for Optimality
146
11
Sufficient Conditions for Optimality
157
2
Convex Problems
159
2
Sensitivity of Optimum Solution to Problem Parameters
161
2
Rosen's Gradient Projection Method for Linear Constraints
163
5
Zoutendijk's Method of Feasible Directions (Nonlinear Constraints)
168
8
The Generalized Reduced Gradient Method (Nonlinear Constraints)
176
7
Sequential Quadratic Programming
183
6
Summary of the Capabilities of Methods for Nonlinear Constrained Problems
189
1
Solved Examples
189
33
Problems
195
8
Computer Programs
203
19
Penalty Function And Duality Based Methods
222
37
Introduction
222
1
Exterior Penalty Functions
222
5
Interior Penalty Functions
227
2
Duality
229
6
The Augmented Lagrangian Method
235
7
Duality and Geometric Programming
242
17
Problems
248
3
Computer Programs
251
8
Direct Search Methods For Nonlinear Optimization
259
37
Introduction
259
1
Cyclic Coordinate Search
259
3
Hooke and Jeeves Pattern Search Method
262
1
Rosenbrock's Method
263
2
Powell's Method of Conjugate Directions
265
1
Nelder and Mead Simplex Method
266
6
Simulated Annealing (SA)
272
4
Genetic Algorithm (GA)
276
3
Box's Complex Method for Constrained Problems
279
4
Conclusion
283
13
Problems
284
2
Computer Programs
286
10
Integer And Discrete Programming
296
31
Introduction
296
2
Zero-One Programming
298
5
Branch and Bound Algorithm for Mixed Integers
303
3
Gomory Cut Method
306
4
Farkas' Method for Discrete Nonlinear Monotone Structural Problems
310
3
Genetic Algorithm for Discrete Programming
313
1
Conclusion
313
14
Problems
313
3
Computer Programs
316
11
Dynamic Programming
327
13
Introduction
327
2
General Definition of the Dynamic Programming Problem
329
3
Problem Modeling and Computer Implementation
332
4
Discussion and Conclusions
336
4
Problems
336
1
Computer Programs
337
3
Optimization Applications For Transportation, Assignment, And Network Problems
340
33
Introduction
340
1
Transportation Problem
340
7
Assignment Problems
347
4
Network Problems
351
5
Conclusion
356
17
Problems
356
3
Computer Programs
359
14
Pareto Optimality
373
12
Introduction
373
1
Concept of Pareto Optimality
374
3
Generation of the Entire Pareto Curve
377
2
A Single Best Compromise Pareto Solution
379
6
Problems
382
3
Finite-Element-Based Optimization
385
44
Introduction
385
1
Parameter Optimization Using Gradient Methods-Derivative Calculations
386
9
Shape Optimization
395
7
Topology Optimization of Continuum Structures
402
6
Optimization with Vibration Response
408
4
Concluding Remarks
412
17
Problems
415
4
Computer Programs
419
10
Index
429