Index

  • a
  • Aberrations
    • Cliffs (vertical walls)
    • Hard to Find Optimum
    • Infeasible Calculations
    • Level Spots
    • Multiple Optima
    • Noise–Stochastic Response
    • of Response Surface
    • Sharp Valleys (or ridges)
    • Striations
    • Uniform Minimum
  • Accelerate
  • Accumulation Along a Path
  • Acknowledgments
  • Acronyms
  • Algebra and Assignment Statements
  • Analytical Method (AM)
    • Issues
  • Annualized Capital
  • a posteriori
  • Appendices
  • Application Classifications
  • a priori
  • Attenuate
  • Autocorrelated
  • b
  • Backward Difference
  • Belongingness
  • Best
  • Best‐of‐N
  • BFGS see Broyden–Fletcher–Goldfarb–Shanno (BFGS)
  • Bisection Method
  • Bloom’s Taxonomy of Cognitive Skill
  • Book, Aspirations
  • Book, aspirations
    • Organization
    • and Style
  • Bootstrapping
    • Appropriating
    • Basis
    • Model uncertainty
    • Result interpretation
  • Bottom Line
  • Broyden–Fletcher–Goldfarb‐Shanno (BFGS)
  • c
  • Canonical optimization statement
  • Case Study
    • Area Coverage
    • Data Reconciliation
    • Goddard Rocket Study
    • In‐Vitro Fertilization
    • Liquid‐Vapor Separator
    • ODE Solution Approximation
    • Pipe System Optimization
    • Queuing
    • Reservoir
    • Retirement
  • Cauchy’s Sequential Line Search (CSLS)
    • Commentary
    • with Golden Section
    • with Heuristic Direct Search
    • with Leapfrogging
    • with Newton/Secant
    • Pseudocode
    • with Successive Quadratic
    • VBA Code
  • CDF see Cumulative distribution function (CDF)
  • Central Difference
  • Central Limit Theorem
  • CG see Conjugate Gradient (CG)
  • Challenge Problems see also Test Functions
  • Challenges to Optimizers
  • CHD see Cyclic Heuristic Direct Search (CHD)
  • Choices
  • Chromosome
  • Classification
    • Application
    • Category OFs
    • Convergence
    • Models
    • Optimization Issues
    • Optimizer
    • Variables
  • Class Variables
    • Random Keys
  • Cliffs Ridges/Valleys
  • CM see Complex Method (CM)
  • Coarse‐Fine Sequence
  • Companion Web Site
  • Compare
    • CHD & HJ
    • CSLS, ISD, NR, LM, RLM, CHD, HJ, LF, PSO
    • CSLS, ISD, SQ, and NR
    • LF, HJ, LM, PSO
    • NR & ISD
    • Optimizers
  • Comparison
    • Convergence Criteria
    • Direct Search w Single Trial Solution
    • Gradient Based
    • Local Surface Characterization Based
    • Multi‐Player Direct Search Optimizers
    • Optimizers and Attributes
  • Complexity Factor
  • Complex Method (CM)
  • Conditionals, Discontinuities
  • Conjugate Gradient (CG)
  • Constituents (Customer Stakeholders)
  • Constraints
    • Active
    • Analysis
    • Equality
    • Equivalent Features
    • Explicit
    • Hard
    • Implicit
    • Inactive
    • Inequality
    • Pass/Fail Categories
    • Penalty Function
    • Penalty Function Soft
    • Slack and Surplus Variables
    • Soft
  • Continuum and Discontinuous DVs
  • Continuum and Discontinuous Models
  • Contour lines
  • Convergence
    • on OF
    • on Change in DV
    • on Change in OF
    • Choosing Threshold Values
    • Classifications
    • on Combinations of Criteria
    • on Comparing Change in OF to Experimental Uncertainty
    • on Comparing Change in OF to Uncertainty in Givens
    • Criteria, Comparison
    • Criteria 1‐D Applications
    • Multiplayer Deterministic
    • on Multi‐Player Range
    • N‐D Criteria
    • Other Criteria
    • premature
    • on Random Subset Sampling
    • on Relative Change in DV
    • on Relative Change in OF
    • on Sensitivity of DV to OF
    • Single TS Deterministic
    • on Steady State
    • Stochastic Applications
  • Convex
  • Criteria
    • Convergence 1‐D Applications
    • for Replicate Trials
    • Stopping 1‐D Applications
  • CSLS see Cauchy’s Sequential Line Search (CSLS)
  • Cumulative Distribution Function (CDF)
  • Customer (Stakeholder, Constituents)
  • Cyclic Heuristic Direct Search (CHD)
    • Pseudocode
    • VBA Code
  • d
  • Decision Variable (DV)
    • Transformations
  • Defining an Iteration
  • Definitions
  • Degree of Freedom
  • Derivative
  • Designing Experiments, test Best‐of‐N
  • Desirables
  • Desired Engineering Attributes
  • Developing/Evolving Application Statements
  • Direct Search
    • Bisection Method
    • Golden Section Method
    • Heuristic Direct Search
    • Leapfrogging
    • LF for Stochastic Functions
    • Multivariable, Multi‐Player
    • Multivariable, Single TS
  • Discontinuities, Conditionals
  • Discontinuous and Continuum
    • DVs
    • Models
  • Discount Factor
  • Discrete and Integer Variables
    • Branch‐and‐Bound
    • Convergence
    • Cyclic Heuristic
    • Exhaustive Search
    • Leapfrogging
    • Multi‐Player
  • Discretization
  • Dominated
  • Do not Study
  • DP see Dynamic Programming (DP)
  • DV see Decision Variable (DV)
  • Dynamic and Static Models
  • Dynamic (transient) Model
  • Dynamic Programming (DP)
    • Concept
    • Conditions
    • Some Calculation Tips
  • e
  • Economic Optimization
    • Annual Cash Flow
    • Capital
    • Combining Capital and Cash Flow
    • Present Value
    • Risk
    • Time Value
    • Uncertainty
  • Effects of Uncertainty
  • Elements Associated with Optimization
  • Enhancements to Optimizers
  • Equal Concern (EC) Weighting
  • Evaluating
  • Evaluating 2nd Order Partial Derivatives
  • Evaluating Optimizers
    • Designing an Experimental Test
    • Metrics of Performance
  • Evaluating Results
  • Evaluating 1st Order Derivatives
  • Experimental OF
  • Exponentially Weighted Moving Average (EWMA)
  • f
  • Feasible
  • Feasible Solutions
  • Final Prediction Error (FPE)
  • First‐Order Filter
  • Fitness
  • Flat spots
  • Forward Differences
  • FPE see Final Prediction Error (FPE)
  • Fuzzy Logic
  • g
  • GA see Genetic/Evolutionary Algorithms (GA)
  • Gamma Function
  • Gauss Elimination
    • Pivoting
    • Procedure
    • VBA Code
  • Gaussian Distributed (NID Box‐Muller)
  • Gene
  • Generalized Reduced Gradient (GRG)
  • Genetic/Evolutionary Algorithms (GA)
    • Fitness of Selection
    • Procedures
  • Givens
  • Global Attractor
  • Global Optimizer
  • Global Optimum
  • Golden Ratio, Side Note
  • Golden Section Method (GS)
  • Gradient
  • Gradient‐Based Optimizers (CSLS and ISD)
  • Gradient Based Optimizer Solutions
  • Greedy Algorithm
  • GRG see Generalized Reduced Gradient (GRG)
  • GS see Golden Section Method (GS)
  • h
  • Hard constraints
  • Heuristic Direct (HD)
    • Pseudocode
  • Hooke‐Jeeves (HJ)
    • VBA Code
  • Human Contrivances
    • Nature Compliance to
  • i
  • Implicit/explicit Relations
  • Incremental Steepest Descent (ISD)
    • Enhanced
    • Illustration
    • Pseudo‐Code
    • VBA Code
  • Inequality Constraints
  • Inflections
  • Initialization Range
  • In‐Process Adjustment of Algorithm Coefficient
  • Integer DV
  • Integers
  • Intellectual Exercise
  • Interval Halving
  • Introductory Concepts
  • Intuitive Decisions
    • Intuitive Optimization
    • Optimization Levels
  • ISD see Incremental Steepest Descent (ISD)
  • Iteration
  • Iterative Procedures
  • k
  • K.I.S.S. Principle
  • l
  • Lagrange‐Type Multiplier
  • Landmark Publications
  • Leapfrogging (LF)
    • Analysis
    • Balance
    • Convergence Criteria
    • Leap‐To Window Amplification
    • Leap‐to Window Translation
    • Minimize NOFE
    • Number of Initializations
    • Premature Convergence
    • Probability Distribution of Leap‐overs
    • Stochastic Functions
  • Levenberg‐Marquardt (LM)
    • Modified (RLM)
    • VBA Code for 2‐DV case
  • LF see Leapfrogging (LF)
  • Linear Algebra Notation
  • Linear Equation Sets
  • Linearity and Nonlinearity
  • Linearizing Data Transform
  • Linear Programming (LP)
    • Algorithm
    • Basic Procedure
    • Canonical Statement
    • Simplex Tableau
  • Line Search (Univariate Search)
  • Linguistic Rules (Fuzzy Logic)
  • LM see Levenberg‐Marquardt (LM)
  • Local Optimum
  • Logistic Model
  • Long Term Return on Assets
  • LP see Linear Programming (LP)
  • m
  • Mathematical Representation of Relations
  • Membership function
  • Memorization, Overfitting
  • Mimetic
  • Min‐Max, Max‐Min
  • Model
    • is wrong
  • Modified Levenberg‐Marquardt (RLM)
    • Pseudo‐Code
    • VBA Code for 2‐DV case
  • Modified OF
    • Impact on NOFE
    • Max‐Min Equivalence
    • Scaling
    • OF Transformation
    • Translating
  • Monte Carlo
  • Multi‐Dimension
  • Multi‐Optima
    • Multiple Starts
  • Multi‐Player
  • Multiple Objectives
    • Additive Combination
    • Classic Weighting Factors
    • Constraint Applications
    • Equal Concern Weighting
    • Non‐Additive OF Combinations
    • Nonlinear Weighting
    • Pareto Optimal
  • Multiple Starts
    • Best‐of‐N
    • Other Options
    • a posteriori Method
    • a priori Method
    • Snyman and Fatti Criterion
  • Multivariate Search
  • Mutation
  • n
  • Nature Compliance to Human Contrivances
  • N‐D Notation
  • Nelder‐Mead (NM)
  • Nested Optimization
  • Net lines
  • Net Present Value (NPV)
  • Newton Interpolating Polynomial
  • Newton‐Methods
  • Newton Raphson (NR)
    • Attenuate
    • Pseudo Code
    • Quasi‐Newton
    • Tempering
  • Newton‐Secant
    • Root‐Finding
  • NM see Nelder‐Mead (NM)
  • NOFE see Number of Function Evaluations (NOFE)
  • Noisy Steady State
  • Nomenclature
  • Non‐Additive Cost Functions
  • Non‐Convex
  • Non‐Dominated
  • Nonlinear Regression
  • Nonparametric, Statistics
  • Normal Equations (Linear Regression)
  • NPV see Net Present Value (NPV)
  • NR see Newton Raphson (NR)
  • Number of Function Evaluations (NOFE)
  • Number of Independent Trials
  • Number of Players
  • Numerical Derivative, Step Size
  • Numerical Iterative Procedures
  • o
  • Objective Function (OF)
    • Transformations
    • Value
  • OF see Objective Function (OF)
  • Opposing
    • functionalities
    • Ideals
    • trends
  • Optimization
    • Definitions
    • Discrete and Integer Variables
    • Introduction
    • Issues
    • Key Points
    • Probable Outcomes and Distribution Characteristics
    • Procedure
    • Stages
    • Terminology
  • Optimizer
    • Classifications
  • Over‐Specification
    • Linear Relations
    • Optimization
  • p
  • Parameter Correlation
  • Parametric Path Notation
  • Parametric, statistics
  • Pareto Optimal
  • Partial Derivatives 1st Order
  • Particle Swarm Optimization (PSO)
    • Equation Analysis
    • Individual Particle Behavior
    • Position Mode
    • Velocity mode
  • Path
    • Accumulation
    • Analysis
    • Integral
    • Parametric Notation
    • Slope
  • Pay‐Back Time
  • Penalty Functions
  • Perfection/Sufficiency
  • Persistence Time‐Constant
  • Perspective on Many topics
  • Phantom (fortuitous) OF value
  • PNOFE see Probable Number of Function Evaluations (PNOFE)
  • Point Values
  • Positional Invariance, “Theory” of
  • Precision
  • Preface
  • Present Value
  • Pretend
  • Primer for VBA Programming
  • Probable Number of Function Evaluations (PNOFE)
  • Probable Outcomes and Distribution Characteristics
  • Probable Outcomes, Stochastic Approach
  • Procedures, not Equations
  • Proficiency
  • Proximity (Vicinity)
  • PSO see Particle Swarm Optimization (PSO)
  • Publications, Landmark
  • q
  • Quasi‐Newton
  • r
  • Random Keys Method
    • Dichotomous Variables
    • Sequence
  • Rank
  • Realization
  • Recursion Formula
  • Reduced Gradient
  • References
  • Regression
    • Akaho’s Method
    • Convergence Criterion
    • Least Squares
    • Maximum Likelihood
    • Model Order or Complexity
    • Models that are Nonlinear in DVs
    • Models with Delay as a DV
    • Normal Least Squares
    • Total Least Squares
    • Vertical Least Squares
  • Reliability
  • Replicates
  • Replicate Trials, Criteria
  • Response Surface Aberrations see also Aberrations
  • Risk
  • RLM see Modified Levenberg–Marquardt (RLM)
  • Rms see root mean square (rms)
  • Root‐Finding
    • on derivative
    • w.r.t. Optimization
  • root mean square (rms)
  • s
  • Saddle Point
  • Scaled Variables
    • Dimensional Consistency
    • Issues with Primitive Variables
    • Linear Scaling Options
    • Nonlinear Scaling
  • Search Range Adjustment
  • Second‐Order Methods 1‐D
  • Second‐Order model Based Optimizers: SQ & NR
  • SEE see sketch evaluate erase (SEE)
  • SHH see Spendley‐Hext‐Himsworth (SHH)
  • Significant Dates
  • Single TS
  • sketch evaluate erase (SEE)
  • Slack Variable
  • Slope Along a Path
  • Soft Constraints
  • Solution of a System of Linear Equations
  • Solution Precision
  • Spendley‐Hext‐Himsworth (SHH)
  • SQ see Successive Quadratic (SQ)
  • SSID see Steady State Identification in Noisy Signals (SSID)
  • Stage Variable
  • Stakeholder (Constituent Customer)
  • State Variable
  • Static and Dynamic Models
  • Stationary Point
  • Steady State Identification in Noisy Signals (SSID)
    • Alternate Type‐I Error
    • Array Method
    • Coefficient Threshold and Sample Frequency Values
    • Conceptual Model
    • Data autocorrelation
    • Filter Method Code
    • Filter Method Equations
    • R‐Statistic
    • Type‐I Error
    • Type‐II Error
    • VBA Code Array Method
    • VBA Code Filter Method
  • Steady State Model
  • Steepest Descent
  • Stochastic Functions
    • Method For Optimizing
    • Replicate the Apparent Best Player
    • Reporting
    • Steady State Detection
  • Stochastic Surfaces
  • Stopping Criteria
    • Constraint Violation
    • End a Futile Search
    • Execution Error
    • N Iterations
  • Successive Quadratic (SQ)
    • Multivariable
    • Pseudo Code
  • Sufficiency/Perfection
  • Sum of Absolute Value of Deviations
  • Sum of Squared Residuals (Deviations)
  • Surface Aberrations see also Aberrations
  • Surface Analysis
  • Surface and Terms
  • Surplus Variable
  • Surrogate Function
  • Surrogate Population
  • Survival of the fittest
  • Sustainable
  • Symbols
  • t
  • Tabu
  • Tangent to Contour
  • Taylor Series
    • Expansion for a Single Variable
    • Expansion for Multiple Variables
  • Tempering Newton‐Type methods
  • Test Functions
    • Algae Pond
    • ARMA(2,1) Regression
    • Boot Print
    • Boot Print w Pinhole
    • Chemical Reaction
    • Chong Vu’s Normal Regression
    • Classroom Lecture Pattern
    • Cork Board
    • Curved Sharp Valley
    • Frog
    • Goddard Problem
    • H & C Mixing Control
    • Hose Winder
    • Integer Problem
    • Liquid‐Vapor Separator
    • Mountain Path
    • Other Sources
    • Parallel Pumps
    • Parameter Correlation
    • Peaks
    • Rank Model
    • Reliability
    • Reservoir
    • Retirement
    • Robot Soccer
    • Shortest Time
    • Slingshot into Space
    • Solving an ODE
    • Stochastic Boot Print
    • Three Springs
    • Underspecified
    • Windblown
  • Textbooks
    • Optimization
    • Probability and Statistics
    • Simulation
    • Specific Techniques
  • Time Value of Money
  • Transformations OF and DV
  • Transformed DVs
  • Traveling Salesman Problem (TSP)
  • Trial‐and‐Error
  • Trial Solution (TS)
  • Troubleshooting
    • CDF Features
    • Concern Over Results
    • DV* is dependent on Convergence Threshold
    • DV values do not change
    • EXE Error
    • Extreme Values
    • Multiple DV* values for the same OF* Value
    • Multiple Equivalent Solutions
    • OF* is Irreproducible
    • Parameter Correlation
  • TSP
  • Two‐D Parametric Notation
  • u
  • UID see Uniform Distributed (UID)
  • Uncertainty
    • Analytical Method
    • Bootstrapping
    • in DV* and OF*
    • Estimating Values
    • Implicit/explicit Relations
    • Modeling Concept
    • Models for
    • Numerical Method
    • in Optimization
    • Propagating Max Error
    • Propagating on DVs
    • Propagating Probable Error
    • Propagation of Variance
    • Significant Digits
    • Sources
  • Uncertainty Effects
  • Under‐Specification
    • Linear Relations
    • Optimization
  • Undesirables
  • Uniform Distributed (UID)
  • Univariate Methods
    • Comparison
  • v
  • Validation
  • Variable Classification
    • Cardinal
    • Discretization
    • Nominal
    • Ordinal
    • Scaled
  • VBA
    • Calling Solver from VBA
    • Conditionals
    • Debugging
    • External File I/O
    • I/O to Excel Cells
    • Keystroke Macros
    • Loops
    • Objects and Properties
    • Operations
    • Primer
    • Run buttons (Commands)
    • Solver Add‐In
    • Variable Types and Declarations
  • w
  • Websites
    • Additional References
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