Related papers: Lagrangian Duality in 3D SLAM: Verification Techni…
Monocular simultaneous localization and mapping (SLAM) is emerging in advanced driver assistance systems and autonomous driving, because a single camera is cheap and easy to install. Conventional monocular SLAM has two major challenges…
We have proposed, to the best of our knowledge, the first-of-its-kind LiDAR-Inertial-Visual-Fused simultaneous localization and mapping (SLAM) system with a strong place recognition capacity. Our proposed SLAM system is consist of…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…
SLAM technology plays a crucial role in indoor mapping and localization. A common challenge in indoor environments is the "double-sided mapping issue", where closely positioned walls, doors, and other surfaces are mistakenly identified as a…
We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is…
Mapping and self-localization in unknown environments are fundamental capabilities in many robotic applications. These tasks typically involve the identification of objects as unique features or landmarks, which requires the objects both to…
We study a class of optimization problems in which the objective function is given by the sum of a differentiable but possibly nonconvex component and a nondifferentiable convex regularization term. We introduce an auxiliary variable to…
Navigation solutions suitable for cases when both autonomous robot's pose (\textit{i.e}., attitude and position) and its environment are unknown are in great demand. Simultaneous Localization and Mapping (SLAM) fulfills this need by…
We propose fast and communication-efficient optimization algorithms for multi-robot rotation averaging and translation estimation problems that arise from collaborative simultaneous localization and mapping (SLAM), structure-from-motion…
This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably…
Object-level Simultaneous Localization and Mapping (SLAM), which incorporates semantic information for high-level scene understanding, faces challenges of under-constrained optimization due to sparse observations. Prior work has introduced…
Among the abilities that autonomous mobile robots should exhibit, map building and localization are definitely recognized as fundamental. Consequently, countless algorithms for solving the Simultaneous Localization And Mapping (SLAM)…
This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. Such constraints arise in many science and engineering domains, where the task amounts to learning optimization problems…
We present a dense simultaneous localization and mapping (SLAM) method that uses 3D Gaussians as a scene representation. Our approach enables interactive-time reconstruction and photo-realistic rendering from real-world single-camera RGBD…
This paper presents a method for robust optimization for online incremental Simultaneous Localization and Mapping (SLAM). Due to the NP-Hardness of data association in the presence of perceptual aliasing, tractable (approximate) approaches…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
We study deterministic and stochastic primal-dual sub-gradient algorithms for distributed optimization of a separable objective function with global inequality constraints. In both algorithms, the norm of the Lagrangian multipliers are…