SIAM conference on Optimization location:Boston, MA, USA date:10-13 May 2008
We present geometric optimization algorithms that approximate
solutions of matrix equations by low-rank SPD matrices. By exploiting
the fact that the set of rank constrained SPD 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.