Contact Laura

SDP Relaxation paper in SIMAX

April 19, 2025 By Laura Balzano

I’m excited that our paper “A Semidefinite Relaxation for Sums of Heterogeneous Quadratic Forms on the Stiefel Manifold” has been published in the SIAM Journal on Matrix Analysis and Applications. https://doi.org/10.1137/23M1545136. We were inspired to work on this problem after it popped up inside the heteroscedastic PCA problem. It’s a fascinating, simple, general problem with connections to PCA, joint diagonalization, and low-rank semidefinite programs. Applying the standard Schur relaxation to this problem gives a trivial (and incorrect) solution, but one minor change makes the relaxation powerful and even tight in many instances. You can find the code for experiments here.