Related papers: Lagrangian Duality in 3D SLAM: Verification Techni…
This paper introduces a novel and distributed method for detecting inter-map loop closure outliers in simultaneous localization and mapping (SLAM). The proposed algorithm does not rely on a good initialization and can handle more than two…
We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…
Simultaneous Localization and Mapping (SLAM) is considered an ever-evolving problem due to its usage in many applications. Evaluation of SLAM is done typically using publicly available datasets which are increasing in number and the level…
We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…
Active Simultaneous Localization and Mapping (SLAM) is the problem of planning and controlling the motion of a robot to build the most accurate and complete model of the surrounding environment. Since the first foundational work in active…
Most Simultaneous localisation and mapping (SLAM) systems have traditionally assumed a static world, which does not align with real-world scenarios. To enable robots to safely navigate and plan in dynamic environments, it is essential to…
Simultaneous Localization and Mapping (SLAM) is a critical task in robotics, enabling systems to autonomously navigate and understand complex environments. Current SLAM approaches predominantly rely on geometric cues for mapping and…
In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…
We propose a visual SLAM method by predicting and updating line flows that represent sequential 2D projections of 3D line segments. While feature-based SLAM methods have achieved excellent results, they still face problems in challenging…
Simultaneous Localization and Mapping (SLAM) has been considered as a solved problem thanks to the progress made in the past few years. However, the great majority of LiDAR-based SLAM algorithms are designed for a specific type of payload…
In this paper, we employ the concept of quasi-relative interior to analyze the method of Lagrange multipliers and establish strong Lagrangian duality for nonsmooth convex optimization problems in Hilbert spaces. Then, we generalize the…
We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagrangian methods in the infinite dimensional setting. Our goal…
Zero-One Composite Optimization (0/1-COP) is a prototype of nonsmooth, nonconvex optimization problems and it has attracted much attention recently. The augmented Lagrangian Method (ALM) has stood out as a leading methodology for such…
Visual SLAM (Simultaneous Localization and Mapping) based on planar features has found widespread applications in fields such as environmental structure perception and augmented reality. However, current research faces challenges in…
Non-convex functional constrained optimization problems have gained substantial attention in machine learning and data science, addressing broad requirements that typically go beyond the often performance-centric objectives. An influential…
Factor graphs are a very powerful graphical representation, used to model many problems in robotics. They are widely spread in the areas of Simultaneous Localization and Mapping (SLAM), computer vision, and localization. In this paper we…
Simultaneous mapping and localization (SLAM) in an real indoor environment is still a challenging task. Traditional SLAM approaches rely heavily on low-level geometric constraints like corners or lines, which may lead to tracking failure in…
This paper is concerned with augmented Lagrangian methods for the treatment of fully convex composite optimization problems. We extend the classical relationship between augmented Lagrangian methods and the proximal point algorithm to the…
Simultaneous localization and mapping is essential for position tracking and scene understanding. 3D Gaussian-based map representations enable photorealistic reconstruction and real-time rendering of scenes using multiple posed cameras. We…
The Augmented Lagrangian Method (ALM) is an iterative method for the solution of equality-constrained non-linear programming problems. In contrast to the quadratic penalty method, the ALM can satisfy equality constraints in an exact way.…