Dummy variable in loop

[Marc Wijnand]

I construct constraints inside a for loop. As this constraints involve Minkowski differences, I have to use dummy variables (see 'w' in this text).

Is it sufficient to define one sdpvar w outside of the loop and use this variable in each iteration, or should I define a matrix of different w's and use another one in each iteration?

SKETCH:

X = ...;

x = sdpvar(2,N);

w = sdpvar(2,1);

for i=1:N

  constraints=[constraints ismember(x(:,i)+w,X)];

end

[Johan Löfberg]

Is it the same variable or different variables? If it is the same w, you can define it outside loop. If it is different w, you can either define w as a matrix and index it, or define a new w variable inside the loop every iteration

[Marc Wijnand]

It are different variables (that are used in optimize() later on), so I will define w as a matrix.

_____

Just to be sure: is it possible to reuse an sdpvar in constraint set definitions?

It works for this example:

x = sdpvar(2,1);

P = eye(2);

Set1=[x'*P*x<=1];

Set2=[x'*P*x<=2];

plot(Set1)

plot(Set2)

[Johan Löfberg]

Not sure what the question is, but perhaps this is the answer

x = sdpvar(2,1);

P = -1 <= x <= 2;

Q = 3 <= x <= 4;

% Plot the two sets

plot(P);plot(Q)

% The set involving both P and Q is of course empty, as the same x is used  in both

plot([P,Q])

[Marc Wijnand]

Thank you for the quick reply.
You define the set X1

x=sdpvar(2,1);
P=eye(2);
X1=[x'*P*x<=1];

and afterwards

X2=[x'*P*x<=2];

The question was if x obtains any properties during the X1 definition that would cause the X2 definition to be invalid. Then it would be necessary to use two separate sdpvariables:

x=sdpvar(2,1);
y=sdpvar(2,1);
X1=[x'*P*x<=1];
X2=[y'*P*y<=2]; %Typo corrected

Or is it safe to reuse x?

[Johan Löfberg]

A variable does not have any reference to which constraints it is being used in