Table of contents:
1 Introduction to Optimization 1 --
1.1 Requirements for the Application of Optimization Methods 2 --
1.1.1 Defining the System Boundaries 2 --
1.1.2 Performance Criterion 3 --
1.1.3 Independent Variables 4 --
1.1.4 System Model 5 --
1.2 Applications of Optimization in Engineering 6 --
1.2.1 Design Applications 8 --
1.2.2 Operations and Planning Applications 15 --
1.2.3 Analysis and Data Reduction Applications 20 --
1.2.4 Classical Mechanics Applications 26 --
1.2.5 Taguchi System of Quality Engineering 27 --
1.3 Structure of Optimization Problems 28 --
2 Functions of a Single Variable 32 --
2.1 Properties of Single-Variable Functions 32 --
2.2 Optimality Criteria 35 --
2.3 Region Elimination Methods 45 --
2.3.1 Bounding Phase 46 --
2.3.2 Interval Refinement Phase 48 --
2.3.3 Comparison of Region Elimination Methods 53 --
2.4 Polynomial Approximation or Point Estimation Methods 55 --
2.4.1 Quadratic Estimation Methods 56 --
2.4.2 Successive Quadratic Estimation Method 58 --
2.5 Methods Requiring Derivatives 61 --
2.5.1 Newton-Raphson Method 61 --
2.5.2 Bisection Method 63 --
2.5.3 Secant Method 64 --
2.5.4 Cubic Search Method 65 --
2.6 Comparison of Methods 69 --
3 Functions of Several Variables 78 --
3.1 Optimality Criteria 80 --
3.2 Direct-Search Methods 84 --
3.2.1 The S[superscript 2] (Simplex Search) Method 86 --
3.2.2 Hooke-Jeeves Pattern Search Method 92 --
3.2.3 Powell's Conjugate Direction Method 97 --
3.3 Gradient-Based Methods 108 --
3.3.1 Cauchy's Method 109 --
3.3.2 Newton's Method 111 --
3.3.3 Modified Newton's Method 115 --
3.3.4 Marquardt's Method 116 --
3.3.5 Conjugate Gradient Methods 117 --
3.3.6 Quasi-Newton Methods 123 --
3.3.7 Trust Regions 127 --
3.3.8 Gradient-Based Algorithm 128 --
3.3.9 Numerical Gradient Approximations 129 --
3.4 Comparison of Methods and Numerical Results 130 --
4 Linear Programming 149 --
4.1 Formulation of Linear Programming Models 149 --
4.2 Graphical Solution of Linear Programs in Two Variables 154 --
4.3 Linear Program in Standard Form 158 --
4.3.1 Handling Inequalities 159 --
4.3.2 Handling Unrestricted Variables 159 --
4.4 Principles of the Simplex Method 161 --
4.4.1 Minimization Problems 172 --
4.4.2 Unbounded Optimum 173 --
4.4.3 Degeneracy and Cycling 174 --
4.4.4 Use of Artificial Variables 174 --
4.4.5 Two-Phase Simplex Method 176 --
4.5 Computer Solution of Linear Programs 177 --
4.5.1 Computer Codes 177 --
4.5.2 Computational Efficiency of the Simplex Method 179 --
4.6 Sensitivity Analysis in Linear Programming 180 --
4.7 Applications 183 --
4.8 Additional Topics in Linear Programming 183 --
4.8.1 Duality Theory 184 --
4.8.2 Dual Simplex Method 188 --
4.8.3 Interior Point Methods 189 --
4.8.4 Integer Programming 205 --
4.8.5 Goal Programming 205 --
5 Constrained Optimality Criteria 218 --
5.1 Equality-Constrained Problems 218 --
5.2 Lagrange Multipliers 219 --
5.3 Economic Interpretation of Lagrange Multipliers 224 --
5.4 Kuhn-Tucker Conditions 225 --
5.4.1 Kuhn-Tucker Conditions or Kuhn-Tucker Problem 226 --
5.4.2 Interpretation of Kuhn-Tucker Conditions 228 --
5.5 Kuhn-Tucker Theorems 229 --
5.6 Saddlepoint Conditions 235 --
5.7 Second-Order Optimality Conditions 238 --
5.8 Generalized Lagrange Multiplier Method 245 --
5.9 Generalization of Convex Functions 249 --
6 Transformation Methods 260 --
6.1 Penalty Concept 261 --
6.1.1 Various Penalty Terms 262 --
6.1.2 Choice of Penalty Parameter R 277 --
6.2 Algorithms, Codes, and Other Contributions 279 --
6.3 Method of Multipliers 282 --
6.3.1 Penalty Function 283 --
6.3.2 Multiplier Update Rule 283 --
6.3.3 Penalty Function Topology 284 --
6.3.4 Termination of the Method 285 --
6.3.5 MOM Characteristics 286 --
6.3.6 Choice of R-Problem Scale 289 --
6.3.7 Variable Bounds 289 --
6.3.8 Other MOM-Type Codes 293 --
7 Constrained Direct Search 305 --
7.1 Problem Preparation 306 --
7.1.1 Treatment of Equality Constraints 306 --
7.1.2 Generation of Feasible Starting Points 309 --
7.2 Adaptations of Unconstrained Search Methods 309 --
7.2.1 Difficulties in Accommodating Constraints 310 --
7.2.2 Complex Method 312 --
7.3 Random-Search Methods 322 --
7.3.1 Direct Sampling Procedures 322 --
7.3.2 Combined Heuristic Procedures 326 --
8 Linearization Methods for Constrained Problems 336 --
8.1 Direct Use of Successive Linear Programs 337 --
8.1.1 Linearly Constrained Case 337 --
8.1.2 General Nonlinear Programming Case 346 --
8.1.3 Discussion and Applications 355 --
8.2 Separable Programming 359 --
8.2.1 Single-Variable Functions 359 --
8.2.2 Multivariable Separable Functions 362 --
8.2.3 Linear Programming Solutions of Separable Problems 364 --
8.2.4 Discussion and Applications 368 --
9 Direction Generation Methods Based on Linearization 378 --
9.1 Method of Feasible Directions 378 --
9.1.1 Basic Algorithm 380 --
9.1.2 Active Constraint Sets and Jamming 383 --
9.2 Simplex Extensions for Linearly Constrained Problems 388 --
9.2.1 Convex Simplex Method 389 --
9.2.2 Reduced Gradient Method 399 --
9.2.3 Convergence Acceleration 403 --
9.3 Generalized Reduced Gradient Method 406 --
9.3.1 Implicit Variable Elimination 406 --
9.3.2 Basic GRG Algorithm 410 --
9.3.3 Extensions of Basic Method 419 --
9.3.4 Computational Considerations 427 --
9.4 Design Application 432 --
9.4.1 Problem Statement 433 --
9.4.2 General Formulation 434 --
9.4.3 Model Reduction and Solution 437 --
10 Quadratic Approximation Methods for Constrained Problems 450 --
10.1 Direct Quadratic Approximation 451 --
10.2 Quadratic Approximation of the Lagrangian Function 456 --
10.3 Variable Metric Methods for Constrained Optimization 464 --
10.4.1 Problem Scaling 470 --
10.4.2 Constraint Inconsistency 470 --
10.4.3 Modification of H[superscript (t)] 471 --
10.4.4 Comparison of GRG with CVM 471 --
11 Structured Problems and Algorithms 481 --
11.1 Integer Programming 481 --
11.1.1 Formulation of Integer Programming Models 482 --
11.1.2 Solution of Integer Programming Problems 484 --
11.1.3 Guidelines on Problem Formulation and Solution 492 --
11.2 Quadratic Programming 494 --
11.2.1 Applications of Quadratic Programming 494 --
11.2.2 Kuhn-Tucker Conditions 498 --
11.3 Complementary Pivot Problems 499 --
11.4 Goal Programming 507 --
12 Comparison of Constrained Optimization Methods 530 --
12.1 Software Availability 530 --
12.2 A Comparison Philosophy 531 --
12.3 Brief History of Classical Comparative Experiments 533 --
12.3.1 Preliminary and Final Results 535 --
13 Strategies for Optimization Studies 542 --
13.1 Model Formulation 543 --
13.1.1 Levels of Modeling 544 --
13.1.2 Types of Models 548 --
13.2 Problem Implementation 552 --
13.2.1 Model Assembly 553 --
13.2.2 Preparation for Solution 554 --
13.2.3 Execution Strategies 580 --
13.3 Solution Evaluation 588 --
13.3.1 Solution Validation 589 --
13.3.2 Sensitivity Analysis 590 --
14 Engineering Case Studies 603 --
14.1 Optimal Location of Coal-Blending Plants by Mixed-Integer Programming 603 --
14.1.1 Problem Description 604 --
14.1.2 Model Formulation 604 --
14.1.3 Results 609 --
14.2 Optimization of an Ethylene Glycol-Ethylene Oxide Process 610 --
14.2.1 Problem Description 610 --
14.2.2 Model Formulation 612 --
14.2.3 Problem Preparation 618 --
14.2.4 Discussion of Optimization Runs 618 --
14.3 Optimal Design of a Compressed Air Energy Storage System 621 --
14.3.1 Problem Description 621 --
14.3.2 Model Formulation 622 --
14.3.3 Numerical Results 627 --
Appendix A Review of Linear Algebra 633 --
A.1 Set Theory 633 --
A.2 Vectors 633 --
A.3 Matrices 634 --
A.3.1 Matrix Operations 635 --
A.3.2 Determinant of a Square Matrix 637 --
A.3.3 Inverse of a Matrix 637 --
A.3.4 Condition of a Matrix 639 --
A.3.5 Sparse Matrix 639 --
A.4 Quadratic Forms 640 --
A.4.1 Principal Minor 641 --
A.4.2 Completing the Square 642 --
A.5 Convex Sets 646 --
Appendix B Convex and Concave Functions 648 --
Appendix C Gauss-Jordan Elimination Scheme 651.

Summary:
The classic introduction to engineering optimization theory and practice--now expanded and updated Engineering optimization helps engineers zero in on the most effective, efficient solutions to problems. This text provides a practical, real-world understanding of engineering optimization.