Constraints without any variables

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Sometimes when working with complex models, it might happen that some constraints are trivially feasible or infeasible, since they evaluate to a fixed number independent of all decision variables. This can cause problems for YALMIP in some cases.

Consider the following model, where the numbers k and m are constants in your code

sdpvar x y
Constraints = [x >= 1, y >= k*y + m]
optimize(F,obj)


This is a perfectly valid model. Now, let us assume that the magic numbers k and m all of a sudden happen to have the values 1 and 0. This would correspond to the following case

k = 1;
m = 1;
sdpvar x y
Constraints = [x >= 1, y >= k*y + m]
optimize(F,obj)


When concatenating the constraints, MATLAB will first tell YALMIP to evaluate all the expressions. When doing so, YALMIP changes the expressions to x - 1>=0 and y-ky-m\geq 0. The second expression will simply lead to the expression 0>=0, i.e., standard MATLAB code without any YALMIP context, which evaluates to logical(1). Hence, the model will be

Constraints = [x-1 >= 0, logical(1)]
optimize(F,obj)


When encountering such a situation, YALMIP will issue a warning to make the user aware of the situation. An even worse case can occur if, e.g., k=1 and m = 1. We then have the model

Constraints = [x-1 >= 0, -1 >= 0]
optimize(F,obj)


This will issue an error in YALMIP since the model by construction is infeasible.