One Ring to Rule Them All: Certifiably Robust Geometric Perception with Outliers Supplementary Material

M and the set X is compact [3, Definition 3.137, p. 115]. To tackle the non-smoothness of the inner minimization " " is equivalent to an optimization over a binary variable: This concludes the proof for Proposition 5. null In this section, we provide a brief but self-contained explanation to shed light on Lasserre's hierarchy Then the POP (2) can be rewritten as a generalized moment problem. Lasserre's hierarchy is a hierarchy of moment relaxations with increasing relaxation orders In general, Lasserre's hierarchy may achieve tightness only asymptotically ( i.e., The following theorem states a sufficient condition. Theorem A5 is a special case of Theorem 3.11 in [ The uniqueness of the solution comes from the fact that Interior Point Methods solvers ( e.g., SeDuMi) To make our explanation of Lasserre's hierarchy in Section A2.1 more accessible, we show an Let us first introduce the notion of a flat extension. " monomial indicator matrix with rows and columns indexed by A that achieves the minimum distance between set K and set A [12, 1]. PSD cone has a closed-form solution, due to Higham [11].