Engineering optimization: applications, methods and analysis 1st Edition by R. Russell Rhinehart ISBN 1118936337 9781118936337

Section 1: Introductory Concepts

1. Optimization 1.1. Optimization and Terminology
   1.2. Optimization Concepts and Definitions
   1.3. Examples
   1.4. Terminology Continued
   1.5. Optimization Procedure
   1.6. Issues That Shape Optimization Procedures
   1.7. Opposing Trends
   1.8. Uncertainty
   1.9. Over‐ and Under‐specification in Linear Equations
   1.10. Over‐ and Under‐specification in Optimization
   1.11. Test Functions
   1.12. Significant Dates in Optimization
   1.13. Iterative Procedures
   1.14. Takeaway
   1.15. Exercises

2. Optimization Application Diversity and Complexity 2.1. Optimization
   2.2. Nonlinearity
   2.3. Min, Max, Min–Max, Max–Min
   2.4. Integers and Other Discretization
   2.5. Conditionals and Discontinuities: Cliffs Ridges/Valleys
   2.6. Procedures, Not Equations
   2.7. Static and Dynamic Models
   2.8. Path Integrals
   2.9. Economic Optimization and Other Nonadditive Cost Functions
   2.10. Reliability
   2.11. Regression
   2.12. Deterministic and Stochastic
   2.13. Experimental w.r.t. Modeled OF
   2.14. Single and Multiple Optima
   2.15. Saddle Points
   2.16. Inflections
   2.17. Continuum and Discontinuous DVs
   2.18. Continuum and Discontinuous Models
   2.19. Constraints and Penalty Functions
   2.20. Ranks and Categorization: Discontinuous OFs
   2.21. Underspecified OFs
   2.22. Takeaway
   2.23. Exercises

3. Validation 3.1. Introduction
   3.2. Validation
   3.3. Advice on Becoming Proficient
   3.4. Takeaway
   3.5. Exercises

Section 2: Univariate Search Techniques

4. Univariate (Single DV) Search Techniques 4.1. Univariate (Single DV)
   4.2. Analytical Method of Optimization
   4.3. Numerical Iterative Procedures
   4.4. Direct Search Approaches
   4.5. Perspectives on Univariate Search Methods
   4.6. Evaluating Optimizers
   4.7. Summary of Techniques
   4.8. Takeaway
   4.9. Exercises

5. Path Analysis 5.1. Introduction
   5.2. Path Examples
   5.3. Perspective About Variables
   5.4. Path Distance Integral
   5.5. Accumulation along a Path
   5.6. Slope along a Path
   5.7. Parametric Path Notation
   5.8. Takeaway
   5.9. Exercises

6. Stopping and Convergence Criteria: 1-D Applications 6.1. Stopping versus Convergence Criteria
   6.2. Determining Convergence
   6.3. Combinations of Convergence Criteria
   6.4. Choosing Convergence Threshold Values
   6.5. Precision
   6.6. Other Convergence Criteria
   6.7. Stopping Criteria to End a Futile Search
   6.8. Choices!
   6.9. Takeaway
   6.10. Exercises

Section 3: Multivariate Search Techniques

7. Multidimensional Application Introduction and the Gradient 7.1. Introduction
   7.2. Illustration of Surface and Terms
   7.3. Some Surface Analysis
   7.4. Parametric Notation
   7.5. Extension to Higher Dimension
   7.6. Takeaway
   7.7. Exercises

8. Elementary Gradient‐Based Optimizers 8.1. Introduction
   8.2. Cauchy’s Sequential Line Search
   8.3. Incremental Steepest Descent
   8.4. Takeaway
   8.5. Exercises

9. Second‐Order Model‐Based Optimizers 9.1. Introduction
   9.2. Successive Quadratic
   9.3. Newton–Raphson
   9.4. Perspective on CSLS, ISD, SQ, and NR
   9.5. Choosing Step Size for Numerical Estimate of Derivatives
   9.6. Takeaway
   9.7. Exercises

10. Gradient‐Based Optimizer Solutions 10.1. Introduction
    10.2. Levenberg–Marquardt (LM)
    10.3. Scaled Variables
    10.4. Conjugate Gradient (CG)
    10.5. Broyden–Fletcher–Goldfarb–Shanno (BFGS)
    10.6. Generalized Reduced Gradient (GRG)
    10.7. Takeaway
    10.8. Exercises

11. Direct Search Techniques 11.1. Introduction
    11.2. Cyclic Heuristic Direct (CHD) Search
    11.3. Hooke–Jeeves (HJ)
    11.4. Compare and Contrast CHD and HJ Features: A Summary
    11.5. Nelder–Mead (NM) Simplex: Spendley, Hext, and Himsworth
    11.6. Multiplayer Direct Search Algorithms
    11.7. Leapfrogging
    11.8. Particle Swarm Optimization
    11.9. Complex Method (CM)
    11.10. A Brief Comparison
    11.11. Takeaway
    11.12. Exercises

Section 4: Developing Your Application Statements

19. Scaled Variables and Dimensional Consistency 19.1. Introduction
    19.2. A Scaled Variable Approach
    19.3. Sampling of Issues with Primitive Variables
    19.4. Linear Scaling Options
    19.5. Nonlinear Scaling
    19.6. Takeaway
    19.7. Exercises

20. Economic Optimization 20.1. Introduction
    20.2. Annual Cash Flow
    20.3. Including Risk as an Annual Expense
    20.4. Capital
    20.5. Combining Capital and Nominal Annual Cash Flow
    20.6. Combining Time Value and Schedule of Capital and Annual Cash Flow
    20.7. Present Value
    20.8. Including Uncertainty
    20.9. Takeaway
    20.10. Exercises

21. Multiple OF and Constraint Applications 21.1. Introduction
    21.2. Solution 1: Additive Combinations of the Functions
    21.3. Solution 2: Nonadditive OF Combinations
    21.4. Solution 3: Pareto Optimal
    21.5. Takeaway
    21.6. Exercises

22. Constraints 22.1. Introduction
    22.2. Equality Constraints
    22.3. Inequality Constraints
    22.4. Constraints: Pass/Fail Categories
    22.5. Hard Constraints Can Block Progress
    22.6. Advice
    22.7. Constraint‐Equivalent Features
    22.8. Takeaway
    22.9. Exercises

Section 5: Perspective on Many Topics

30. Perspective 30.1. Introduction
    30.2. Classifications
    30.3. Elements Associated with Optimization
    30.4. Root Finding Is Not Optimization
    30.5. Desired Engineering Attributes
    30.6. Overview of Optimizers and Attributes
    30.7. Choices
    30.8. Variable Classifications
    30.9. Constraints
    30.10. Takeaway
    30.11. Exercises

Section 6: Analysis of Leapfrogging Optimization

35. Analysis of Leapfrogging 35.1. Introduction
    35.2. Balance in an Optimizer
    35.3. Number of Initializations to be Confident That the Best Will Draw All Others to the Global Optimum
    35.4. Leap‐To Window Amplification Analysis
    35.5. Analysis of α and M to Prevent Convergence on the Side of a Hill
    35.6. Analysis of α and M to Minimize NOFE
    35.7. Probability Distribution of Leap‐Overs
    35.8. Takeaway
    35.9. Exercises

Section 7: Case Studies

36. Case Study 1 36.1. Process and Analysis
    36.2. Exercises

37. Case Study 2 37.1. The Process and Analysis
    37.2. Exercises

38. Case Study 3 38.1. The Process and Analysis
    38.2. Exercises

39. Case Study 4 39.1. The Process and Analysis
    39.2. Pre‐Assignment Note
    39.3. Exercises

40. Case Study 5 40.1. The Process and Analysis
    40.2. Exercises

41. Case Study 6 41.1. Description and Analysis
    41.2. Exercises

42. Case Study 7 42.1. Concepts and Analysis
    42.2. Exercises

43. Case Study 8 43.1. Description and Analysis
    43.2. Exercises

44. Case Study 9 44.1. Description and Analysis
    44.2. Exercises

45. Case Study 10 45.1. Description and Analysis
    45.2. Exercises

Section 8: Appendices

• Appendix content not listed, but likely includes supplementary information, data, and tools related to optimization.