# Glossary

- Function
- A mathematical expression for a response variable in terms of design variables. Often used interchangeably with “response”. Symbolized by f.
- Function evaluation
- Using a solver to analyze a single design and produce a result. See Simulation.
- Functionally efficient
- See Pareto optimal.
- Global approximation
- A design function which is representative of the entire design space.
- Global Optimization
- The mathematical procedure for finding the global optimum in the design space. E.g. Genetic Algorithm, Particle Swarm, etc.
- Global variable
- A variable of which the scope spans across all the design disciplines or solvers. Used in the MDO context.
- Gradient vector
- A vector consisting of the derivatives of a function f in terms of a number of variables x1 to xn. s = [df /dxi]. See Design Sensitivity.
- GSA
- See Global Sensitivity Analysis.
- History
- Response history containing two columns of (usually time) data generated by a simulation.
- Importance
- See Weight.
- Infeasible Design
- A design which does not comply with the constraint functions. An entire design space or region of interest can sometimes be infeasible.
- Iteration
- A cycle involving an experimental design, function evaluations of the designs, approximation and optimization of the approximate problem.
- Kriging
- A Metamodeling technique using Bayesian regression. (see e.g. [5,23]).
- Latin Hypercube Sampling
- The use of a constrained random experimental design as a point selection scheme for response approximation.
- Least Squares Approximation
- The determination of the coefficients in a mathematical expression so that it approximates certain experimental results by the minimization of the sum of the squares of the approximation errors. Used to determine response surfaces as well as calibrating analysis models.
- Local Approximation
- See Gradient vector.
- Local variable
- A variable of which the scope is limited to a particular discipline or disciplines. Used in the MDO context.
- Material identification
- See parameter identification.
- MDO
- Multidisciplinary design optimization.
- Metamodeling
- The construction of surrogate design models such as polynomial response surfaces, Artificial Neural Networks or Kriging surfaces from simulations at a set of design points.
- Min-Max optimization problem
- An optimization problem in which the maximum value considering several responses or functions is minimized.
- Model calibration
- The optimal adjustment of parameters in a numerical model to simulate the physical model as closely as possible.
- Modeling error
- See bias error.
- MOO
- Multi-objective Optimization
- MP
- Mathematical Programming. Mathematical optimization.
- MSE
- Mean Squared Error. Used for system identification.
- Multi-objective
- An objective function which is constituted of more than one objective. Symbolized by F. Multi-criteria. Refers to optimization problems in which several criteria are considered.
- Multidisciplinary design optimization (MDO)
- The inclusion of multiple disciplines in the design optimization process. In general, only some design variables need to be shared between the disciplines to provide limited coupling in the optimization of a multidisciplinary target or objective.
- Neural network approximation
- The use of trained feedforward neural networks to perform non-linear regression, thereby constructing a non-linear response surface.
- Noise
- See random error.