Reklaitis' name appears first on the earlier edition.

Includes bibliographical references and indexes.

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.

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