most recent 30 from http://mathoverflow.net 2013-05-22T13:18:31Z http://mathoverflow.net/feeds/question/82279 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/82279/semidefinite-program-with-varying-objective-function Kap 2011-11-30T14:37:34Z 2011-11-30T14:37:34Z

<p>Assume a real semidefinite program $\min_X trace(BX)$ subject to $trace(A_jX) \geq c$, $j = 1\ldots m$, for some constant $c$, where $A_j$ are of rank one. Now $B$ is positive definite with fixed eigenvalues, but one is able to vary the orthogonal matrix in $B$ freely. Is anything known about where the optimal solution occurs for such a problem? Any results about varying semidefinite programs? Thanks.</p>