Related papers: Convex Relaxations for Pose Graph Optimization wit…

This paper studies an optimization problem on the sum of traces of matrix quadratic forms in $m$ semi-orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the…

This work provides a theoretical analysis for optimally solving the pose estimation problem using total least squares for vector observations from landmark features, which is central to applications involving simultaneous localization and…

Robustly estimating camera poses from a set of images is a fundamental task which remains challenging for differentiable methods, especially in the case of small and sparse camera pose graphs. To overcome this challenge, we propose…

We explore the connection between outlier-robust high-dimensional statistics and non-convex optimization in the presence of sparsity constraints, with a focus on the fundamental tasks of robust sparse mean estimation and robust sparse PCA.…

We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…

We derive a convex optimization problem for the task of segmenting sequential data, which explicitly treats presence of outliers. We describe two algorithms for solving this problem, one exact and one a top-down novel approach, and we…

Semidefinite Programming (SDP) and Sums-of-Squares (SOS) relaxations have led to certifiably optimal non-minimal solvers for several robotics and computer vision problems. However, most non-minimal solvers rely on least-squares…

Outlier-robust estimation is a fundamental problem and has been extensively investigated by statisticians and practitioners. The last few years have seen a convergence across research fields towards "algorithmic robust statistics", which…

Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…

Finding efficient and provable methods to solve non-convex optimization problems is an outstanding challenge in machine learning and optimization theory. A popular approach used to tackle non-convex problems is to use convex relaxation…

How to efficiently and accurately handle image matching outliers is a critical issue in two-view relative estimation. The prevailing RANSAC method necessitates that the minimal point pairs be inliers. This paper introduces a linear relative…

The estimation of the camera poses associated with a set of images commonly relies on feature matches between the images. In contrast, we are the first to address this challenge by using objectness regions to guide the pose estimation…

We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a…

Range-only (RO) pose estimation involves determining a robot's pose over time by measuring the distance between multiple devices on the robot, known as tags, and devices installed in the environment, known as anchors. The nonconvex nature…

We address the sensor network localization problem given noisy range measurements between pairs of nodes. We approach the non-convex maximum-likelihood formulation via a known simple convex relaxation. We exploit its favorable optimization…

The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…

We present a novel method for global motion planning of robotic systems that interact with the environment through contacts. Our method directly handles the hybrid nature of such tasks using tools from convex optimization. We formulate the…

We consider a category-level perception problem, where one is given 3D sensor data picturing an object of a given category (e.g. a car), and has to reconstruct the pose and shape of the object despite intra-class variability (i.e. different…

Convex relaxations of the AC power flow equations have attracted significant interest in the power systems research community in recent years. The following collection of video lectures provides a brief introduction to the mathematics of AC…

Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…