Engineering Optimization

Preface.

1 Introduction to Optimization.

1.1 Requirements for the Application of Optimization Methods.

1.2 Applications of Optimization in Engineering.

1.3 Structure of Optimization Problems.

1.4 Scope of This Book.

References.

2 Functions of a Single Variable.

2.1 Properties of Single-Variable Functions.

2.2 Optimality Criteria.

2.3 Region Elimination Methods.

2.4 Polynomial Approximation or Point Estimation Methods.

2.5 Methods Requiring Derivatives.

2.6 Comparison of Methods.

2.7 Summary.

References.

Problems.

3 Functions of Several Variables.

3.1 Optimality Criteria.

3.2 Direct-Search Methods.

3.3 Gradient-Based Methods.

3.4 Comparison of Methods and Numerical Results.

3.5 Summary.

References.

Problems.

4 Linear Programming.

4.1 Formulation of Linear Programming Models.

4.2 Graphical Solution of Linear Programs in Two Variables.

4.3 Linear Program in Standard Form.

4.5 Computer Solution of Linear Programs.

4.5.1 Computer Codes.

4.6 Sensitivity Analysis in Linear Programming.

4.7 Applications.

4.8 Additional Topics in Linear Programming.

4.9 Summary.

References.

Problems.

5 Constrained Optimality Criteria.

5.1 Equality-Constrained Problems.

5.2 Lagrange Multipliers.

5.3 Economic Interpretation of Lagrange Multipliers.

5.4 Kuhn-Tucker Conditions.

5.5 Kuhn-Tucker Theorems.

5.6 Saddlepoint Conditions.

5.7 Second-Order Optimality Conditions.

5.8 Generalized Lagrange Multiplier Method.

5.9 Generalization of Convex Functions.

5.10 Summary.

References.

Problems.

6 Transformation Methods.

6.1 Penalty Concept.

6.2 Algorithms, Codes, and Other Contributions.

6.3 Method of Multipliers.

6.4 Summary.

References.

Problems.

7 Constrained Direct Search.

7.1 Problem Preparation.

7.2 Adaptations of Unconstrained Search Methods.

7.3 Random-Search Methods.

7.4 Summary.

References.

Problems.

8 Linearization Methods for Constrained Problems.

8.1 Direct Use of Successive Linear Programs.

8.2 Separable Programming.

8.3 Summary.

References.

Problems.

9 Direction Generation Methods Based on Linearization.

9.1 Method of Feasible Directions.

9.2 Simplex Extensions for Linearly Constrained Problems.

9.3 Generalized Reduced Gradient Method.

9.4 Design Application.

9.5 Summary.

References.

Problems.

10 Quadratic Approximation Methods for Constrained Problems.

10.1 Direct Quadratic Approximation.

10.2 Quadratic Approximation of the Lagrangian Function.

10.3 Variable Metric Methods for Constrained Optimization.

10.4 Discussion.

10.5 Summary.

References.

Problems.

11 Structured Problems and Algorithms.

11.1 Integer Programming.

11.2 Quadratic Programming.

11.3 Complementary Pivot Problems.

11.4 Goal Programming.

11.5 Summary.

References.

Problems.

12 Comparison of Constrained Optimization Methods.

12.1 Software Availability.

12.2 A Comparison Philosophy.

12.3 Brief History of Classical Comparative Experiments.

12.4 Summary.

References.

13 Strategies for Optimization Studies.

13.1 Model Formulation.

13.2 Problem Implementation.

13.3 Solution Evaluation.

13.4 Summary.

References.

Problems.

14 Engineering Case Studies.

14.1 Optimal Location of Coal-Blending Plants by Mixed-Integer

Programming.

14.2 Optimization of an Ethylene Glycol-Ethylene Oxide Process.

14.3 Optimal Design of a Compressed Air Energy Storage System.

14.4 Summary.

References.

Appendix A Review of Linear Algebra.

A.1 Set Theory.

A.2 Vectors.

A.3 Matrices.

A.3.1 Matrix Operations.

A.3.2 Determinant of a Square Matrix.

A.3.3 Inverse of a Matrix.

A.3.4 Condition of a Matrix.

A.3.5 Sparse Matrix.

A.4 Quadratic Forms.

A.4.1 Principal Minor.

A.4.2 Completing the Square.

A.5 Convex Sets.

Appendix B Convex and Concave Functions.

Appendix C Gauss-Jordan Elimination Scheme.

Author Index.

Subject Index.