Solving graph equipartition SDPs on an algebraic variety

In this paper, we focus on using the low-rank factorization approach to solve SDP relaxation of a graph equipartition problem, which involves an additional spectral upper bound over traditional linear SDP. We discuss equivalence between decomposed problem and original problem. also derive sufficient condition, under second order stationary point non-convex is global minimum. Moreover, constraints involve algebraic variety with conducive geometric properties analyse. develop method escape from non-optimal singular variety. This allows us use Riemannian optimization techniques very efficiently certified optimality.