Task 
Theory 
QuickField 
% 
linear1. Move square's right edge to the right in order to get the maximal crosssection area. The movement range is 0..1
The optimized value is linearly dependent upon the optimization parameter. 
2 
1.9981 
0.1% 
linear2. Move square's right and top edges right and up correspondingly in order to get the maximal crosssection area. The movement range for each edge is 0..1.
The optimized value is linearly dependent upon two optimization parameters. 
4 
3.9836 
0.41% 
linear3. Move square's 3 edges (right, left and top) in order to get the maximal crosssection area. The movement range for each edge is 0..1.
The optimized value is linearly dependent upon three optimization parameters. 
6 
5.9674 
0.54% 
linear1_2. Move square's right edge by its two vertices moving right independently in order to get the maximal crosssection area. The movement range for each vertex is 0..1.
The optimized value is linearly dependent upon two optimization parameters. 
2 
1.9967 
0.17% 
linear1_11. There are 11 squares (like the one in task linear1). Move each square's right edge in order to get the maximal total crosssection area. Each edge can be moved independently. All in all there are 11 optimization parameters.
The optimized value is linearly dependent upon 11 optimization parameters. 
22 
21.928 
0.33% 

square1. Move halfcircle's right vertex in order to get the maximal crosssection area. The movement range is 0..1.
The optimized value is square dependent upon the optimization parameter. 
3.5343 
3.5271 
0.2% 
cubic1. The same as previous. Axisymmetric model represents sphere. The sphere volume is calculated. The movement range is 0..1.
The optimized value is cubic dependent on the optimization parameter 
14.1372 
14.094 
0.31% 

nonlinear1. Move common boundary 11 of rectangle and halfcircle in order to get the minimal area.
Half circle cross section is S1=π/2·(x/2)^{2}.
The rectangle cross section is S2=0.5·(1x).
The optimal parameter value is x=2/π. 
0.6366 
0.6366 
0.00% 
nonlinear2. The same as previous but the volume of sphere and cylinder is minimized.
The sphere volume is V1=4π/3·(x/2)^{3}. Rectangle in axisymmetric model represents a cylinder. Its volume can be calculated as V2=π·0.5^{2}·(1x).
The optimal parameter value is x=1/sqrt(2). 
0.7071 
0.7059 
0.17% 
nonlinear3. Minimization of the total length of the lines connecting the internal point of the rectangle with its vertices. Optimal position of the internal point should be in the intersection of the diagonals. 
5.6569 
5.6569 
0.00% 