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| Preface to the Second Edition | |
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| Notation | |
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| Optimization Models | |
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| Mathematical Modeling | |
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| The System Concept | |
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| Hierarchical Levels | |
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| Mathematical Models | |
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| Elements of Models | |
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| Analysis and Design Models | |
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| Decision Making | |
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| Design Optimization | |
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| The Optimal Design Concept | |
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| Formal Optimization Models | |
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| Multicriteria Models | |
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| Nature of Model Functions | |
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| The Question of Design Configuration | |
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| Systems and Components | |
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| Hierarchical System Decomposition | |
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| Feasibility and Boundedness | |
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| Feasible Domain | |
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| Boundedness | |
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| Activity | |
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| Topography of the Design Space | |
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| Interior and Boundary Optima | |
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| Local and Global Optima | |
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| Constraint Interaction | |
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| Modeling and Computation | |
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| Design Projects | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| Model Construction | |
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| Modeling Data | |
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| Graphical and Tabular Data | |
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| Families of Curves | |
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| Numerically Generated Data | |
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| Best Fit Curves and Least Squares | |
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| Neural Networks | |
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| Kriging | |
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| Modeling a Drive Screw Linear Actuator | |
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| Assembling the Model Functions | |
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| Model Assumptions | |
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| Model Parameters | |
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| Negative Null Form | |
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| Modeling an Internal Combustion Engine | |
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| Flat Head Chamber Design | |
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| Compound Valve Head Chamber Design | |
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| Design of a Geartrain | |
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| Model Development | |
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| Model Summary | |
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| Model Reduction | |
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| Modeling Considerations Prior to Computation | |
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| Natural and Practical Constraints | |
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| Asymptotic Substitution | |
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| Feasible Domain Reduction | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| Model Boundedness | |
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| Bounds, Extrema, and Optima | |
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| Well-Bounded Functions | |
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| Nonminimizing Lower Bound | |
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| Multivariable Extension | |
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| Air Tank Design | |
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| Constrained Optimum | |
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| Partial Minimization | |
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| Constraint Activity | |
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| Cases | |
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| Underconstrained Models | |
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| Monotonicity | |
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| First Monotonicity Principle | |
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| Criticality | |
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| Optimizing a Variable Out | |
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| Adding Constraints | |
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| Recognizing Monotonicity | |
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| Simple and Composite Functions | |
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| Integrals | |
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| Inequalities | |
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| Conditional Criticality | |
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| Multiple Criticality | |
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| Dominance | |
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| Relaxation | |
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| Uncriticality | |
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| Equality Constraints | |
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| Equality and Activity | |
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| Replacing Monotonic Equalities by Inequalities | |
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| Directing an Equality | |
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| Regional Monotonicity of Nonmonotonic Constraints | |
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| Variables Not in the Objective | |
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| Hydraulic Cylinder Design | |
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| A Monotonicity Principle for Nonobjective Variables | |
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| Nonmonotonic Functions | |
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| Model Preparation Procedure | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| Interior Optima | |
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| Existence | |
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| The Weierstrass Theorem | |
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| Sufficiency | |
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| Local Approximation | |
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| Taylor Series | |
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| Quadratic Functions | |
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| Vector Functions | |
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| Optimality | |
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| First-Order Necessity | |
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| Second-Order Sufficiency | |
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| Nature of Stationary Points | |
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| Convexity | |
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| Convex Sets and Functions | |
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| Differentiable Functions | |
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| Local Exploration | |
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| Gradient Descent | |
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| Newton's Method | |
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| Searching along a Line | |
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| Gradient Method | |
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| Modified Newton's Method | |
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| Stabilization | |
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| Modified Cholesky Factorization | |
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| Trust Regions | |
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| Moving with Trust | |
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| Trust Region Algorithm | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| Boundary Optima | |
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| Feasible Directions | |
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| Describing the Constraint Surface | |
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| Regularity | |
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| Tangent and Normal Hyperplanes | |
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| Equality Constraints | |
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| Reduced (Constrained) Gradient | |
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| Lagrange Multipliers | |
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| Curvature at the Boundary | |
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| Constrained Hessian | |
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| Second-Order Sufficiency | |
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| Bordered Hessians | |
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| Feasible Iterations | |
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| Generalized Reduced Gradient Method | |
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| Gradient Projection Method | |
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| Inequality Constraints | |
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| Karush-Kuhn-Tucker Conditions | |
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| Lagrangian Standard Forms | |
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| Geometry of Boundary Optima | |
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| Interpretation of KKT Conditions | |
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| Interpretation of Sufficiency Conditions | |
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| Linear Programming | |
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| Optimality Conditions | |
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| Basic LP Algorithm | |
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| Sensitivity | |
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| Sensitivity Coefficients | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| Parametric and Discrete Optima | |
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| Parametric Solution | |
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| Particular Optimum and Parametric Procedures | |
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| Branching | |
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| Graphical Interpretation | |
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| Parametric Tests | |
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| The Monotonicity Table | |
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| Setting up | |
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| First New Table: Reduction | |
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| Second New Table: Two Directions and Reductions | |
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| Third New Table: Final Reduction | |
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| Branching by Conditional Criticality | |
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| The Stress-Bound Cases | |
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| Parametric Optimization Procedure | |
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| Functional Monotonicity Analysis | |
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| Explicit Algebraic Elimination | |
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| Implicit Numerical Solution | |
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| Optimization Using Finite Element Analysis | |
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| Discrete Variables | |
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| Discrete Design Activity and Optimality | |
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| Constraint Activity Extended | |
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| Discrete Local Optima | |
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| Transformer Design | |
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| Model Development | |
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| Preliminary Set Constraint Tightening | |
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| Constraint Derivation | |
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| Discriminant Constraints | |
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| Constraint Addition | |
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| Linear and Hyberbolic Constraints | |
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| Further Upper and Lower Bound Generation | |
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| Case Analysis | |
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| Constraint Substitution: Remaining Cases | |
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| Relaxation and Exhaustive Enumeration | |
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| Continuous Relaxation: Global Lower Bounds | |
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| Problem Completion: Exhaustive Enumeration | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| Local Computation | |
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| Numerical Algorithms | |
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| Local and Global Convergence | |
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| Termination Criteria | |
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| Single Variable Minimization | |
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| Bracketing, Sectioning, and Interpolation | |
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| The Davies, Swann, and Campey Method | |
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| Inexact Line Search | |
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| Quasi-Newton Methods | |
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| Hessian Matrix Updates | |
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| The DFP and BFGS Formulas | |
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| Active Set Strategies | |
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| Adding and Deleting Constraints | |
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| Lagrange Multiplier Estimates | |
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| Moving along the Boundary | |
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| Penalties and Barriers | |
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| Barrier Functions | |
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| Penalty Functions | |
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| Augmented Lagrangian (Multiplier) Methods | |
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| Sequential Quadratic Programming | |
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| The Lagrange-Newton Equations | |
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| Enhancements of the Basic Algorithm | |
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| Solving the Quadratic Subproblem | |
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| Trust Regions with Constraints | |
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| Relaxing Constraints | |
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| Using Exact Penalty Functions | |
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| Modifying the Trust Region and Accepting Steps | |
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| Yuan's Trust Region Algorithm | |
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| Convex Approximation Algorithms | |
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| Convex Linearization | |
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| Moving Asymptotes | |
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| Choosing Moving Asymptotes and Move Limits | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| Principles and Practice | |
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| Preparing Models for Numerical Computation | |
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| Modeling the Constraint Set | |
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| Modeling the Functions | |
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| Modeling the Objective | |
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| Computing Derivatives | |
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| Finite Differences | |
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| Automatic Differentiation | |
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| Scaling | |
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| Interpreting Numerical Results | |
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| Code Output Data | |
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| Degeneracy | |
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| Selecting Algorithms and Software | |
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| Partial List of Software Packages | |
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| Partial List of Internet Sites | |
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| Optimization Checklist | |
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| Problem Identification | |
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| Initial Problem Statement | |
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| Analysis Models | |
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| Optimal Design Model | |
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| Model Transformation | |
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| Local Iterative Techniques | |
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| Final Review | |
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| Concepts and Principles | |
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| Model Building | |
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| Model Analysis | |
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| Local Searching | |
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| Summary | |
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| Notes | |
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| References | |
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| Author Index | |
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| Subject Index | |