Related papers: Generalized Proximal Methods for Pose Graph Optimi…
Bayesian optimization (BO) is a powerful framework for optimizing expensive black-box objectives, yet extending it to graph-structured domains remains challenging due to the discrete and combinatorial nature of graphs. Existing approaches…
In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes. At a…
The proximal stochastic gradient method (PSGD) is one of the state-of-the-art approaches for stochastic composite-type problems. In contrast to its deterministic counterpart, PSGD has been found to have difficulties with the correct…
Pose Graph Optimization involves the estimation of a set of poses from pairwise measurements and provides a formalization for many problems arising in mobile robotics and geometric computer vision. In this paper, we consider the case in…
This article introduces a novel method for object-level relocalization of robotic systems. It determines the pose of a camera sensor by robustly associating the object detections in the current frame with 3D objects in a lightweight…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
We develop model-based methods for solving stochastic convex optimization problems, introducing the approximate-proximal point, or aProx, family, which includes stochastic subgradient, proximal point, and bundle methods. When the modeling…
Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric information of the data by…
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…
A regularized optimization problem over a large unstructured graph is studied, where the regularization term is tied to the graph geometry. Typical regularization examples include the total variation and the Laplacian regularizations over…
In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
The 1-median problem (1MP) on undirected weighted graphs seeks to find a facility location minimizing the total weighted distance to all customer nodes. Although the 1MP can be solved exactly by computing the single-source shortest paths…
Map-based LiDAR pose tracking is essential for long-term autonomous operation, where onboard map priors need be compact for scalable storage and fast retrieval, while online observations are often partial, repetitive, and heavily occluded.…
Inferring the posterior distribution in SLAM is critical for evaluating the uncertainty in localization and mapping, as well as supporting subsequent planning tasks aiming to reduce uncertainty for safe navigation. However, real-time full…
We propose a novel approach for fast and accurate stereo visual Simultaneous Localization and Mapping (SLAM) independent of feature detection and matching. We extend monocular Direct Sparse Odometry (DSO) to a stereo system by optimizing…
In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the induced primal-dual regularization, the authors propose to…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
The stochastic subgradient method is a widely-used algorithm for solving large-scale optimization problems arising in machine learning. Often these problems are neither smooth nor convex. Recently, Davis et al. [1-2] characterized the…
In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…