Looking at semidefinite programs, are there any sufficient conditions for the solvability (i.e. the optimal value can be achieved, that is infimum=minimum)?


Obviously if the problem is unbounded, the optimal value cannot be attained.
Also, if my objective function is continous and the domain is compact, everything is fine, right?


Any help or hint to literature would be appreciated.



When can the optimal value of a SDP be achieved?
If the primal problem is feasible and its *dual* problem possesses a *strictly feasible* point, i.e. a point belonging to the (relative) interior of the feasible region, then the primal problem


* is bounded
* attains its optimal value at some point
* has no duality gap with its dual


(note however that under these hypotheses the dual itself is not guaranteed to attain its optimal value).


