Illinois-Type Methods for Noisy Euclidean Distance Realization

In this work, we introduce an iterative algorithm for the Euclidean distance matrix completion (EDMC) problem with noisy and incomplete distance measurements. The proposed method is based on semidefinite programming, utilizes a Pareto iterative approach, and performs a projection-free convex optimization over the spectrahedron to solve a level-set problem relevant to EDMC problems. The optimality trade-off between the trace of a positive semidefinite matrix and a loss function is pursued over Pareto optimal points with simple, derivative-free, costly efficient nonlinear equation root finding iterations called Illinois-type methods. We evaluate our approach numerically in a scenario where distance measurements are affected by multiplicative noise.