On the local stability of semidefinite relaxations

We consider a parametric family of quadratically constrained quadratic programs and their associated semidefinite programming (SDP) relaxations. Given nominal value the parameter at which SDP relaxation is exact, we study conditions (and quantitative bounds) under will continue to be exact as moves in neighborhood around value. Our framework captures wide array statistical estimation problems including tensor principal component analysis, rotation synchronization, orthogonal Procrustes, camera triangulation resectioning, essential matrix estimation, system identification, approximate GCD. results can also used analyze stability SOS relaxations general polynomial optimization problems.