Determining the vertices of a polytopic Yalmip constraint set

[Marc Wijnand]

After some calculations, I obtained a Yalmip constraint set that is in fact a polytope and I want to know the coordinates of its vertices. Using the 'Data cursor' in the Figure window, I can inspect the values and manually enter them in a matrix. How can I do this in an automatic way?

x = sdpvar(2,1);

X = [-1<=x<=1];

plot(X,x)

   xlim([-2 2])

   ylim([-2 2])

[Johan Löfberg]

You have to convert to a mpt object

[Marc Wijnand]

If you know the matrices A,b in Ax<=b (such as in the MWE above), it is straightforward to use an MPT Polyhedron. However, I have situations where a yalmip constraint set appears to be polytopic, but I don't have the matrices. My problem is whether it is possible to determine the vertices of such a yalmip set.

[Johan Löfberg]

The only thing you can do is to extract the points on the inner approximation of the feasible set that YALMIP computed

W =plot(...)

[Marc Wijnand]

This works.

x = sdpvar(2,1);

X = [-1<=x<=1];

%plot(X,x)

%   xlim([-2 2])

%   ylim([-2 2])

%hold on

pointlist = plot(X,x);

pointlist = cell2mat(pointlist);

pointlist = (unique(pointlist','rows','stable'))'

pointlist = [pointlist pointlist(:,1)] %close figure

%plot(pointlist(1,:),pointlist(2,:))

[Marc Wijnand]

BTW, this is also the way to 'convert' a nonpolytopic yalmip constraint set to a polytope: extract the vertices via the plot command and define an MPT Polytope with them.