OPTEC SAB meeting edition:2 location:Leuven date:17 March 2008
In this work we develop geometric optimization algorithms that approximate solutions of matrix equations by low-rank symmetric semidefinite matrices. By exploiting the fact that the set of rank constrained symmetric semidefinite matrices is a smooth manifold, we can lift the cost function to the tangent space of the manifold. This allows us to circumvent the curse of dimensionality involved in these matrix equations. The geometry and implementation of the manifold as well as trust-region methods are discussed.