Error Bounds and Singularity Degree in Semidefinite Programming

In semidefinite programming a proposed optimal solution may be quite poor in spite of having sufficiently small residual in the optimality conditions. This issue may be framed in terms of the discrepancy between forward error (the unmeasurable `true error’) and backward error (the measurable violation of optimality conditions). In his seminal work, Sturm provided an … Read more

Noisy Euclidean Distance Matrix Completion with a Single Missing Node

We present several solution techniques for the noisy single source localization problem, i.e.,~the Euclidean distance matrix completion problem with a single missing node to locate under noisy data. For the case that the sensor locations are fixed, we show that this problem is implicitly convex, and we provide a purification algorithm along with the SDP … Read more

Complete Facial Reduction in One Step for Spectrahedra

A spectrahedron is the feasible set of a semidefinite program, SDP, i.e., the intersection of an affine set with the positive semidefinite cone. While strict feasibility is a generic property for random problems, there are many classes of problems where strict feasibility fails and this means that strong duality can fail as well. If the … Read more