[Csdp] initial solution

[Brian Borchers]

>I wonder if I could use just a primal solution as an initial solution  
>(as opposed to a primal and dual initial solutions), and if so how to  
>indicate it to CSDP (in the command line).

There's no option in the code that would allow this.  You can provide an
initial primal/dual solution in a file and give it to csdp as the third
argument on the command line.  

In general, you shouldn't expect the primal-dual method to perform very
well from an aribtrary starting position.  It can very easily perform 
badly if either of the initial primal or dual solutions are too close to the
boundary of the cone of positive semidefinite matrices.  

The algorithm has to start with some primal/dual solution in which the
X and Z matrices are strictly positive definite.  The linear equality
constraints do not have to be satisfied by the initial solution.  If
you have a primal solution that you want to start with but no dual
solution, you could try using your X together with y=0, Z=I (or some
scaled version of the identity) to see what happens.