The question 

The question I would like to set up a design of experiments for the two factors A and B. However, I do not know how to take into account the following constraints: 

• A can be varied as desired
• B must either be 0 or it must hold that B>2*A is

The answer 

The core problem here is that most DOE programs do not allow an "or" function when formulating constraints. However, the real problem is not a software one. In fact, the experimental setup described would lead to difficulties in evaluating the experimental design. Let us first visualize the desired area of investigation: 

There are actually two independent areas of investigation: 

• In the first area, the factor B must be kept at a value of 0, while the value of A can be varied as desired. In the graphic this is shown as the horizontal green line. 
• The second area - the green triangle in the upper left area of the graph - represents the constraint B>2*A. Let's manually set up a DOE for a quadratic model. This could then look like this:

While this solution is not wrong in a purely formal sense, a problem arises in the interpretation of the resulting regression model: It is the nature of regression models to interpolate. The regression model is fitted to the existing data bridging the empty regions in space. 

The graph above visualizes the space covered by the regression model in blue/purple. The problem here is especially the purple area. The model interpolates between the test points on the lower right (A=1 and B=0) and on the upper right (A=0.5 and B=1). This connection is an important part in estimating the influence of B on the target variable.   Thus, our model is based in part on the assumption that it makes sense to assume a connection along this axis. However, since we have formulated constraints that avoid experiments exactly in this range, we have to assume that this assumption does not make sense for technical reasons.  

Proposed solution