# OS-E: 0925 Solve an Optimization Problem Not Defined by a Finite Element Model

This example involves the optimization of a box defined entirely by equations (there is no finite element model in the solution).

## Model Files

Refer to Access the Model Files to download the required model file(s).

The model file used in this example includes:

box.fem

## Model Description

The optimization problem is defined as:
Objective
Maximize the volume of a cube AxBxC
Constraint
The surface of the cube should be between 2.0 and 3.0
Design Variables
A, B, C
The volume and surface are defined as equations using DRESP2 and DEQATN:
 VOLUME
$DEQATN 1 VOL(W,L,H)=W*L*H$
$SURFACE$
DEQATN  2       AREA(W,L,H)=2.0*(W*H+L*H+W*L)
$DRESP2 1 VOLUME 1 DESVAR 1 2 3 DRESP2 2 SURFACE 2 DESVAR 1 2 3$
DESVAR  1       W       1.1     0.1     10.0
DESVAR  2       L       0.9     0.1     10.0
DESVAR  3       H       2.0     0.1     10.0
\$

Then, in the optimization problem, the objective and constraint are global responses (for example, DESOBJ and DESGLB are used outside of a SUBCASE).

To trick OptiStruct into solving this problem, a dummy finite element model must be provided. Here, a single shell element with some load is used.

## Results

As expected, the solution yields a cube with even sides of about 0.707, a surface of 3.0, and a volume of 3.53.