Applied optimization with MATLAB programming

Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... Pamukkale Merkez Kütüphanesi	Kitap	0033233	QA402.5.V42 2002	Searching... Unknown
Searching... Pamukkale Merkez Kütüphanesi	Kitap	0033252	QA402.5.V42 2002	Searching... Unknown

A new approach to learning classical optimization methods-numerical techniques modeled and illustrated via MATLAB

This unique and timely volume combines a formal presentation of classical methods of design optimization with detailed instruction in the application of these methods using MATLAB. It introduces readers to the symbolic, numerical, and graphic features of MATLAB and integrates this powerful combination in the translation of many algorithms into applied optimization techniques with animation.

Applied Optimization with MATLAB Programming develops all necessary mathematical concepts, illustrates abstract mathematical ideas of optimization using MATLAB's rich graphics features, and introduces new programming skills incrementally as optimization concepts are presented. This valuable learning tool:
* Focuses on real-world optimization techniques
* Covers all areas of optimization, including linear, nonlinear, discrete, and global
* Includes creative examples from many disciplines
* Presents a number of practical, open-ended design problems
* Features an accompanying Web site with MATLAB code for all the numerical techniques and examples in the book

This one-of-a-kind resource enables senior-undergraduate and graduate students in engineering and other design disciplines to develop practical programming skills as they master the concepts of optimization. It is also an excellent self-teaching guide for design engineers in all fields of endeavor.

Author Notes

P. Venkataraman, PhD, is an associate professor in the Mechanical Engineering Department, Rochester Institute of Technology, Rochester, New York.

Preface	p. xiii
1 Introduction	p. 1
1.1 Optimization Fundamentals	p. 3
1.1.1 Elements of Problem Formulation	p. 4
1.1.2 Mathematical Modeling	p. 11
1.1.3 Nature of Solution	p. 18
1.1.4 Characteristics of the Search Procedure	p. 23
1.2 Introduction to Matlab	p. 27
1.2.1 Why Matlab?	p. 28
1.2.2 Matlab Installation Issues	p. 29
1.2.3 Using Matlab the First Time	p. 31
1.2.4 An Interactive Session	p. 33
1.2.5 Using the Editor	p. 36
1.2.6 Creating a Code Snippet	p. 41
1.2.7 Creating a Program	p. 46
1.2.8 Application Bibliography	p. 49
Problems	p. 51
2 Graphical Optimization	p. 67
2.1 Problem Definition	p. 68
2.1.1 Example 2.1	p. 68
2.1.2 Format for the Graphical Display	p. 70
2.2 Graphical Solution	p. 70
2.2.1 Matlab High-Level Graphics Functions	p. 71
2.2.2 Matlab Plot Editor	p. 73
2.2.3 Example 2.1-Graphical Solution	p. 74
2.3 Additional Examples	p. 80
2.3.1 Example 2.2-Different Ways of Displaying Information	p. 80
2.3.2 Example 2.3-Flagpole Design	p. 86
2.3.3 Example 2.4-Fin Design for Heat Transfer Application	p. 97
2.3.4 Example 2.5-Shipping Container with Three Design Variables	p. 106
2.4 Additional Matlab Graphics	p. 118
2.4.1 Handle Graphics	p. 118
2.4.2 Interactive Contour Plots	p. 120
References	p. 126
Problems	p. 126
3 Linear Programming	p. 130
3.1 Problem Definition	p. 131
3.1.1 Standard Format	p. 132
3.1.2 Modeling Issues	p. 136
3.2 Graphical Solution	p. 145
3.2.1 Example 3.1	p. 147
3.2.2 Characteristics of the Solution	p. 150
3.2.3 Different Solution Types	p. 153
3.3 Numerical Solution-The Simplex Method	p. 154
3.3.1 Features of the Simplex Method	p. 154
3.3.2 Application of Simplex Method	p. 156
3.3.3 Solution Using Matlab Code	p. 159
3.3.4 Solution Using Matlab's Optimization Toolbox	p. 161
3.4 Additional Examples	p. 162
3.4.1 Example 3.2-Transportation Problem	p. 162
3.4.2 Example 3.3-Equality Constraints and Unrestricted Variables	p. 169
3.4.3 Example 3.4-A Four-Variable Problem	p. 175
3.5 Additional Topics in Linear Programming	p. 182
3.5.1 Primal and Dual Problem	p. 182
3.5.2 Example 3.5	p. 183
3.5.3 Sensitivity Analysis	p. 195
References	p. 198
Problems	p. 198
4 Nonlinear Programming	p. 203
4.1 Problem Definition	p. 204
4.1.1 Problem Formulation-Example 4.1	p. 205
4.1.2 Additional Optimization Problems	p. 207
4.2 Mathematical Concepts	p. 209
4.2.1 Symbolic Computation Using Matlab	p. 209
4.2.2 Basic Mathematical Concepts	p. 213
4.2.3 Taylor's Theorem/Series	p. 221
4.3 Analytical Conditions	p. 224
4.3.1 Unconstrained Problem	p. 225
4.3.2 Equality-Constrained Problem 2	p. 230
4.3.3 Equality-Constrained Problem 3	p. 236
4.3.4 Inequality-Constrained Optimization	p. 239
4.3.5 A General Optimization Problem	p. 246
4.4 Examples	p. 249
4.4.1 Example 4.2-Curve Fitting	p. 249
4.4.2 Example 4.3-Flagpole Problem	p. 251
4.4.3 Additional Topics	p. 256
References	p. 258
Problems	p. 259
5 Numerical Techniques - The One-Dimensional Problem	p. 261
5.1 Problem Definition	p. 262
5.1.1 Constrained One-Dimensional Problem	p. 262
5.1.2 Necessary and Sufficient Conditions	p. 263
5.1.3 Solution to the Examples	p. 263
5.2 Numerical Techniques	p. 265
5.2.1 Features of the Numerical Techniques	p. 265
5.2.2 Newton-Raphson Technique	p. 266
5.2.3 Bisection Technique	p. 269
5.2.4 Polynomial Approximation	p. 271
5.2.5 Golden Section Method	p. 276
5.3 Importance of the One-Dimensional Problem	p. 279
5.4 Additional Examples	p. 281
5.4.1 Example 5.3-Golden Section Method for Many Variables	p. 281
5.4.2 Example 5.4-Two-Point Boundary Value Problem	p. 283
5.4.3 Example 5.5-Root Finding with Golden Section	p. 286
References	p. 288
Problems	p. 288
6 Numerical Techniques for Unconstrained Optimization	p. 290
6.1 Problem Definition	p. 291
6.1.1 Example 6.1	p. 291
6.1.2 Graphical Solution	p. 291
6.1.3 Necessary and Sufficient Conditions	p. 292
6.1.4 Elements of a Numerical Technique	p. 293
6.2 Numerical Technique-Nongradient Methods	p. 294
6.2.1 Scan and Zoom	p. 294
6.2.2 Random Walk	p. 296
6.2.3 Pattern Search	p. 299
6.2.4 Powell's Method	p. 302
6.3 Numerical Technique-Gradient-Based Methods	p. 306
6.3.1 Steepest Descent Method	p. 306
6.3.2 Conjugate Gradient (Fletcher-Reeves) Method	p. 310
6.3.3 Davidon-Fletcher-Powell Method	p. 313
6.3.4 Broydon-Fletcher-Goldfarb-Shanno (BFGS) Method	p. 317
6.4 Numerical Technique-Second Order	p. 320
6.4.1 Modified Newton's Method	p. 321
6.5 Additional Examples	p. 323
6.5.1 Example 6.2-Rosenbrock Problem	p. 323
6.5.2 Example 6.3-Three-Dimensional Flow near a Rotating Disk	p. 326
6.5.3 Example 6.4-An Electrical Engineering Problem	p. 329
6.6 Summary	p. 332
References	p. 333
Problems	p. 333
7 Numerical Techniques for Constrained Optimization	p. 337
7.1 Problem Definition	p. 338
7.1.1 Problem Formulation-Example 7.1	p. 339
7.1.2 Necessary Conditions	p. 340
7.1.3 Elements of a Numerical Technique	p. 342
7.2 Indirect Methods for Constrained Optimization	p. 343
7.2.1 Exterior Penalty Function (EPF) Method	p. 344
7.2.2 Augmented Lagrange Multiplier Method	p. 349
7.3 Direct Methods for Constrained Optimization	p. 354
7.3.1 Constrained Scan and Zoom	p. 354
7.3.2 Expansion of Functions	p. 359
7.3.3 Sequential Linear Programming (SLP)	p. 363
7.3.4 Sequential Quadratic Programming (SQP)	p. 369
7.3.5 Generalized Reduced Gradient (GRG) Method	p. 377
7.3.6 Sequential Gradient Restoration Algorithm (SGRA)	p. 383
7.4 Additional Examples	p. 389
7.4.1 Example 7.2-Flagpole Problem	p. 390
7.4.2 Example 7.3-I-Beam Design	p. 394
7.4.3 Example 7.4-Box Design	p. 398
References	p. 400
Problems	p. 401
8 Discrete Optimization	p. 403
8.1 Concepts in Discrete Programming	p. 405
8.1.1 Problem Relaxation	p. 406
8.1.2 Discrete Optimal Solution	p. 407
8.2 Discrete Optimization Techniques	p. 409
8.2.1 Exhaustive Enumeration	p. 411
8.2.2 Branch and Bound	p. 414
8.2.3 Dynamic Programming	p. 422
8.3 Additional Examples	p. 427
8.3.1 Example 8.4-I-Beam Design-Single Variable?	p. 427
8.3.2 Zero-One Integer Programming	p. 430
References	p. 435
Problems	p. 435
9 Global Optimization	p. 437
9.1 Problem Definition	p. 438
9.1.1 Global Minimum	p. 439
9.1.2 Nature of the Solution	p. 441
9.1.3 Elements of a Numerical Technique	p. 443
9.2 Numerical Techniques and Additional Examples	p. 445
9.2.1 Simulated Annealing (SA)	p. 445
9.2.2 Genetic Algorithm	p. 457
References	p. 467
Problems	p. 468
10 Optimization Toolbox from Matlab	p. 469
10.1 The Optimization Toolbox	p. 470
10.1.1 Programs	p. 473
10.1.2 Using Programs	p. 476
10.1.3 Setting Optimization Parameters	p. 479
10.2 Examples	p. 481
10.2.1 Linear Programming	p. 481
10.2.2 Quadratic Programming	p. 482
10.2.3 Unconstrained Optimization	p. 484
10.2.4 Constrained Optimization	p. 485
References	p. 488
11 Hybrid Mathematics - An Application	p. 489
11.1 Central Idea	p. 490
11.1.1 Bezier Function-2D	p. 490
11.1.2 Bezier Function-3D	p. 493
11.1.3 Data Decoupling	p. 495
11.1.4 Derivatives	p. 495
11.2 Data-Handling Examples	p. 496
11.2.1 Data Fitting with Bezier Functions	p. 496
11.2.2 Optimum Bezier Solution	p. 497
11.2.3 Example 11.1-Smooth Data at Equidistant Intervals	p. 498
11.2.4 Example 11.2-Data Fitting Using Bezier Surface	p. 500
11.3 Solutions to Differential Systems	p. 503
11.3.1 Flow over a Rotating Disk	p. 504
11.3.2 Two-Dimensional Flow Entering a Channel	p. 509
11.4 Summary	p. 517
References	p. 518
Index	p. 521

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