### Design Variable

A quantity in the MDO problem that is always under the explicit control of an optimizer. Design variables may be local, i.e., pertain to a single discipline, or they may be shared by multiple disciplines.

### Discipline Analysis

Solving a system of equations for a particular discipline. Some examples may include the Navier–Stokes equations in fluid mechanics, the static equilibrium equations in structural mechanics, or the equations of motion in a control simulation. In these example, fluid mechanics, structural mechanics, and control simulation are the **disciplines**.

### State/Response Variables

State variables are the results from discipline analysis that describe the current state of a system. That is, they describe the characteristics of the current system. They are often called response variables.

### Coupling Variables

Exchanged in multidisciplinary systems to model interactions of the whole system. Often, the number of variables exchanged is much smaller than the total number of state variables computed in a particular discipline.

### Models

A model can be seen as a black box which takes input values (which can be design variables or output variables) and produces output values. A model represents a technical knowledge of the relations between different parts of a problem and can be as simple as a linear function or a much more complex algorithm requiring several hours of calculation.

### Constraints

These are strict restrictions on some parts of the problem, represented as functional constraints defined by equalities and/or inequalities.

### Objectives

The end goal. In MDO, objectives are quantified so that an objective function can be produced. The objective function then allows for optimization.

### Mathematical notation for MDO Problem Formulations (Martins and Lambe)

### References

Cramer, Evin J., et al. “On alternative problem formulations for multidisciplinary design optimization.” *proceedings of the fourth aiaa/usaf/nasa/oai symposium on multidisciplinary analysis and optimization*. 1992. link

Cramer, Evin J., et al. “Problem formulation for multidisciplinary optimization.” *SIAM Journal on Optimization* 4.4 (1994): 754-776. link

Martins, Joaquim RRA, and Andrew B. Lambe. “Multidisciplinary design optimization: a survey of architectures.” *AIAA journal* 51.9 (2013): 2049-2075. link

Jorquera, Tom, et al. “Experimenting on a Novel Approach to MDO using an Adaptive Multi-Agent System.” link