دانلود کتاب Optimization concepts and applications in engineering

فهرست مطالب :

Contents......Page 7
Preface......Page 11
1.1 Introduction......Page 16
1.2 Historical Sketch......Page 17
1.3 The Nonlinear Programming Problem......Page 19
1.4 Optimization Problem Modeling......Page 21
1.5 Graphical Solution of One- and Two-Variable Problems......Page 32
1.6 Existence of a Minimum and a Maximum: Weierstrass Theorem......Page 35
1.7 Quadratic Forms and Positive Definite Matrices......Page 37
1.8 Cn Continuity of a Function......Page 38
1.9 Gradient Vector, Hessian Matrix, and their Numerical Evaluation using Divided Differences......Page 39
1.10 Taylor’s Theorem, Linear and Quadratic Approximations......Page 44
1.11 Miscellaneous Topics......Page 46
Chapter 1 Problems......Page 49
Chapter 1 Computer Programs......Page 52
Bibliography......Page 53
Some Optimization Conferences......Page 56
Some Optimization Specific Journals......Page 57
2.2 Theory Related to Single-Variable (Univariate) Minimization......Page 58
2.3 Unimodality and Bracketing the Minimum......Page 65
2.4 Fibonacci Method......Page 67
2.5 Golden Section Search Method......Page 73
2.6 Polynomial-Based Methods......Page 77
2.7 Optimization of Non-unimodal Functions......Page 84
2.9 Zero of a Function......Page 91
Chapter 2 Problems......Page 95
Bibliography......Page 102
3.1 Introduction......Page 103
3.2 Necessary and Sufficient Conditions for Optimality......Page 104
3.3 Convexity......Page 107
3.4 Basic Concepts: Starting Design, Direction Vector, and Step Size......Page 109
3.5 The Steepest Descent Method......Page 111
3.6 The Conjugate Gradient Method......Page 119
3.7 Newton’s Method......Page 123
3.8 Quasi-Newton Methods......Page 127
3.9 Approximate Line Search......Page 132
Chapter 3 Problems......Page 134
Bibliography......Page 140
4.2 Linear Programming Problem......Page 142
4.3 Problem Illustrating Modeling, Solution, Solution Interpretation, and Lagrange Multipliers......Page 143
4.4 Problem Modeling......Page 147
4.5 Geometric Concepts: Hyperplanes, Half-spaces, Polytopes, Extreme Points......Page 152
4.6 Standard Form of an LP......Page 153
4.7 The Simplex Method – Starting with LE (≤) Constraints......Page 155
4.8 Treatment of GE and EQ Constraints......Page 160
4.9 Revised Simplex Method......Page 165
4.10 Duality in Linear Programming......Page 168
4.11 The Dual Simplex Method......Page 171
4.12 Criss-Cross Method......Page 173
4.13 Sensitivity Analysis......Page 176
4.14 Interior Approach......Page 182
4.15 Quadratic Programming (QP) and the Linear Complementary Problem (LCP)......Page 186
Chapter 4 Problems......Page 189
Bibliography......Page 195
5.1 Introduction......Page 197
5.2 Graphical Solution of Two-Variable Problems......Page 200
5.3 Use of Excel SOLVER and MATLAB......Page 201
5.4 Formulation of Problems in Standard NLP Form......Page 203
5.5 Necessary Conditions for Optimality......Page 204
5.6 Sufficient Conditions for Optimality......Page 215
5.7 Convexity......Page 219
5.8 Sensitivity of Optimum Solution to Problem Parameters......Page 221
5.9 Rosen’s Gradient Projection Method for Linear Constraints......Page 224
5.10 Zoutendijk’s Method of Feasible Directions (Nonlinear Constraints)......Page 229
5.11 The Generalized Reduced Gradient Method (Nonlinear Constraints)......Page 238
5.12 Sequential Quadratic Programming (SQP)......Page 247
5.13 Features and Capabilities of Methods Presented in this Chapter......Page 252
Chapter 5 Problems......Page 259
Bibliography......Page 267
6.2 Exterior Penalty Functions......Page 269
6.3 Interior Penalty Functions......Page 274
6.4 Extended Interior Penalty Functions......Page 276
6.5 Duality......Page 277
6.6 The Augmented Lagrangian Method......Page 284
6.7 Geometric Programming......Page 289
Chapter 6 Problems......Page 295
Bibliography......Page 300
7.2 Cyclic Coordinate Search......Page 302
7.3 Hooke and Jeeves Pattern Search Method......Page 305
7.4 Rosenbrock’s Method......Page 308
7.5 Powell’s Method of Conjugate Directions......Page 311
7.6 Nelder and Mead Simplex Method......Page 314
7.7 Simulated Annealing (SA)......Page 320
7.8 Genetic Algorithm (GA)......Page 324
7.9 Differential Evolution (DE)......Page 329
7.10 Box’s Complex Method for Constrained Problems......Page 330
7.11 Transformation of Variables to Remove some Bounds and Constraints......Page 332
Chapter 7 Problems......Page 334
Bibliography......Page 341
8.1 Introduction......Page 343
8.2 Concept of Pareto Optimality......Page 344
8.3 Significance and Generation of the Entire Pareto Surface......Page 347
8.4 Methods to Identify a Single Best Compromise Solution......Page 351
Chapter 8 Problems......Page 360
Bibliography......Page 364
9.1 Introduction......Page 366
9.2 Zero–One Programming......Page 368
9.3 Branch and Bound Algorithm for Mixed Integers (LP-based)......Page 374
9.4 Gomory Cut Method......Page 378
9.5 Farkas’ Method for Discrete Nonlinear Monotone Structural Problems......Page 382
Chapter 9 Problems......Page 385
Bibliography......Page 389
10.1 Introduction......Page 390
10.2 The Dynamic Programming Problem and Approach......Page 392
10.3 Problem Modeling and Computer Implementation......Page 396
Chapter 10 Problems......Page 400
Chapter 10 Computer Programs......Page 402
Bibliography......Page 403
11.2 Transportation Problem......Page 404
11.3 Assignment Problems......Page 411
11.4 Network Problems......Page 415
Chapter 11 Problems......Page 420
Bibliography......Page 423
12.1 Introduction......Page 424
12.2 Derivative Calculations......Page 427
12.3 Sizing (i.e. Parameter) Optimization via Optimality Criteria and Nonlinear Programming Methods......Page 434
12.4 Topology Optimization of Continuum Structures......Page 438
12.5 Shape Optimization......Page 441
12.6 Optimization With Dynamic Response......Page 449
Chapter 12 Problems......Page 455
Chapter 12 Computer Programs......Page 460
Bibliography......Page 461
Index......Page 463