Packages for Semidefinite programming

Question

This question has already been asked here. I am not sure, whether I should have asked this question as a comment of an old question or in the general programming forum of stackexchange. Moderators please read and take appropriate decisions.

My machine is of 32 bit with Ubuntu 14.04. I have managed to install cvxopt, and necessary libraries for 64 bit (as much possible with Ubuntu). While installing pythonika, I am having trouble with the library, even after installing Python 2.6 and necessary interface (which, as a matter of fact loaded a lot of garbage programs - as it seems). (If someone interested, here is the error message given below). As a result, I can not install further programs. I use Mathematica 9.0, though I have backup of 7.0 and 8.0 as well.

The problem I am working is optimizing product of a Hermitian matrix (given) and a positive semi-definite operator with unit trace. I am not particularly interested in graph-theoretic or other aspects of SDP. Is there any ready-made package available which can be implemented directly. Or in worst case, is there any other programme interface which can be used in Mathematica 9 along with my system configuration).

I know that there are packages in Matlab for solving SDP. However, so far all of my programmes are written in Mathematica. I do not have time to learn Matlab and migrate all those programmes in it.

/usr/bin/ld: /usr/local/Wolfram/Mathematica/9.0/SystemFiles/Links/MathLink/DeveloperKit/Linux/CompilerAdditions/libML32i3.a(mlnumenv.c.o): undefined reference to symbol 'fmod@@GLIBC_2.2.5'
//lib/x86_64-linux-gnu/libm.so.6: error adding symbols: DSO missing from command line
collect2: error: ld returned 1 exit status

Answer 1

This add-on is the best I've found: https://github.com/NCAlgebra/NC

The documentation that is more specific to SDPs is here: http://www.math.ucsd.edu/~ncalg/DOCUMENTATION/index.html#SemidefiniteProgramming

Answer 2

Semidefinite programming (see here) has been added to Mathematica 12. Example

(*Dimension of matrices*)
d = 5;
(*Create matrices a0,a1,a2*)
a0 = RandomReal[{-1, 1}, {d, d}];
a0 = a0.Transpose@a0;
a1 = IdentityMatrix@d;
v = RandomReal[{-1, 1}, d];
a2 = TensorProduct[v, v];
a = {a0, a1, a2};
(*Vector c on objective function f = c.x*)
c = {3, 1};
(*Compute solution*)
sol = SemidefiniteOptimization[c, a];
(*Check solution*)
A = a0 + sol.{a1, a2};
ev = Sort@Eigenvalues@A;
q = PositiveSemidefiniteMatrixQ@A;
Print["Minimizer {x1,x2} of c.x such that A = a0+x1*a1+x2*a2 is \
positive semidefinite: \n\t", sol, "\nEigenvalues of A: \n\t", ev, "\n\
Is A positive semidefinite?\n\t", q]