Sparse decision-matrices

[Pontus]

Hi,

I would like to solve the following SDP:

min trace(CX)
X>=A

where X is a real symmetric matrix with a sparsity structure, i.e., many elements in the X-matrix are zero. Is there an efficient way of describing this structure using YALMIP? I have tried to create the X-matrix as a full sdpvar and set elements to zero using equality constraints, this is however very slow. Is there a better way?

/Pontus

[Johan Löfberg]

Imposing many zeros through equalities will not be efficient.

Assume E is a matrix containing the 0/1 sparsity pattern. Then I would do

X = sdpvar(n);
X = X.*E;

An alternative, which is more efficient if X is very large since it avoids the initial symbolic generation, is

[i,j] = find(triu(E));
X = sparse(i,j,sdpvar(length(i),1);X = X+X'-diag(diag(X));