Tutte colloquium-Yuen-Man Pun

Title:What is New in Join-Aggregate Query Processing?

Abstract: : In this talk, we will address the maximum-likelihood (ML) formulation and a least-squares (LS) formulation of the time-of-arrival (TOA)-based source localization problem. Although both formulations are generally non-convex, we will show that they both possess benign optimization landscape. First, we consider the ML formulation of the TOA-based source localization problem. Under standard assumptions on the TOA measurement model, we will show a bound on the distance between an optimal solution and the true target position and establish the local strong convexity of the ML function at its global minima. Second, we consider the LS formulation of the TOA-based source localization problem. We will show that the LS formulation is globally strongly convex under certain condition on the geometric configuration of the anchors and the source and on the measurement noise. We will then derive a characterization of the critical points of the LS formulation, which leads to a bound on the maximum number of critical points under a very mild assumption on the measurement noise and a sufficient condition for the critical points of the LS formulation to be isolated. The said characterization also leads to an algorithm that can find a global optimum of the LS formulation by searching through all critical points. Lastly, we will discuss some possible future directions.