How to include PSD constraint in TFOCS

[Mark_L_Stone]

Do you really wish to use TFCOs as opposed to CVX?

Unfortunately, I don;t believe any of the TFOCS developers are still active on this forum, and doubt there are many or any advanced users of TFOCS still active here. So you may have to figure things out on your own.

Nevertheless, a quick search shows these 2 posts from @Stephen_Becker one of the TFOCS developers, which might help you.

Rank minimization with TFOCS

Here’s a solution for some of the formulations (e.g., A*vec(X) ~= b), with the CVX code and the TFOCS code: n = 10; m = round(n/2); A = randn(m,n^2); b = randn(m,1); epsilon = .1; %% Solve in CVX cvx_begin cvx_precision best variable X(n,n) minimize trace(X) subject to X == semidefinite(n) norm( A*vec(X) - b, Inf ) <= epsilon cvx_end X_CVX = X; %% Solve in TFOCS linear = linop_compose( linop_matrix(A), linop_vec([n,n]) ); affneF = { linear, -b }; objectiveF = prox_trace; dua…

Sparse PCA in TFOCS

Here’s one way to do it. I modified proj_psdUTrace.m to take in an extra trace term (since this is just a linear term). An extra linear term is quite common so we may take care of it nicely in a future release of TFOCS. For now, the modified proj_psdUTrace.m is in github, so head there to get the latest version. First, setup the problem rng(100); d = 20; X = randn(d); R = X'*X; % Sigma e = ones(d,1); lambda = 0.5; Now solve in CVX so we can verify we’re solving the right problem cvx_begin cv…

You can also see all posts on this forum categorized as TFOCS at TFOCS - CVX Forum: a community-driven support forum .