Related papers: Sensor network localization has a benign landscape…
We consider the localization problem of multiple wideband sources in a multi-path environment by coherently taking into account the attenuation characteristics and the time delays in the reception of the signal. Our proposed method leaves…
A common approach to localize a mobile robot is by measuring distances to points of known positions, called anchors. Locating a device from distance measurements is typically posed as a non-convex optimization problem, stemming from the…
We explore the local landscape of low-rank matrix recovery, focusing on reconstructing a $d_1\times d_2$ matrix $X^\star$ with rank $r$ from $m$ linear measurements, some potentially noisy. When the noise is distributed according to an…
We study the problem of signal source localization using received signal strength measurements. We begin by presenting verifiable geometric conditions for sensor deployment that ensure the model's asymptotic localizability. Then we…
This paper focuses on the problem of localising a transmitting mobile station (MS) using multiple cooperative base stations (BSs). There are two technical difficulties: one is the data association between intermediate parameters and…
In this paper we consider the localization problem for a visual sensor network. Inspired by the alternate attitude and position distributed optimization framework discussed in [1], we propose an estimation scheme that exploits the unit dual…
Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…
Low-rank approximation with zeros aims to find a matrix of fixed rank and with a fixed zero pattern that minimizes the Euclidean distance to a given data matrix. We study the critical points of this optimization problem using algebraic…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
Distributed cooperative localization in wireless networks is a challenging problem since it typically requires solving a large-scale nonconvex and nonsmooth optimization problem. In this paper, we reformulate the classic cooperative…
We study the optimization problem associated with fitting two-layer ReLU neural networks with respect to the squared loss, where labels are generated by a target network. We make use of the rich symmetry structure to develop a novel set of…
We present a new approach for computing approximate global minimizers to a large class of non-local pairwise interaction problems defined over probability distributions. The approach predicts candidate global minimizers, with a recovery…
Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…
The reliable operation of large-scale electric power networks is increasingly challenging, particularly with the integration of stochastic renewable generation. In this work, we address the problem of minimizing network transients by…
In recent years, there has been remarkable progress in the development of so-called certifiable perception methods, which leverage semidefinite, convex relaxations to find global optima of perception problems in robotics. However, many of…
This paper analytically characterizes optimal sensor placements for target localization and tracking in 2D and 3D. Three types of sensors are considered: bearing-only, range-only, and received-signal-strength. The optimal placement problems…
Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…