Related papers: Memory Optimization for Convex Hull Support Point …

Vehicle pose estimation with LiDAR is essential in the perception technology of autonomous driving. However, due to incomplete observation measurements and sparsity of the LiDAR point cloud, it is challenging to achieve satisfactory pose…

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…

Let $P$ be a planar set of $n$ points in general position. We consider the problem of computing an orientation of the plane for which the Rectilinear Convex Hull of $P$ has minimum area. Bae et al. (Computational Geometry: Theory and…

We study a natural extension to the well-known convex hull problem by introducing multiplicity: if we are given a set of convex polygons, and we are allowed to partition the set into multiple components and take the convex hull of each…

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…

In this paper we present several results on the expected complexity of a convex hull of $n$ points chosen uniformly and independently from a convex shape. (i) We show that the expected number of vertices of the convex hull of $n$ points,…

An algorithm is developed to optimize vehicle speed trajectory over multiple signalized intersections with known traffic signal information to minimize fuel consumption and travel time, and to meet ride comfort requirements using sequential…

Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…

Chan [JACM, 2010] gave a data structure for maintaining the convex hull of a dynamic set of 3D points under insertions and deletions, supporting extreme-point queries. Subsequent refinements by Kaplan, Mulzer, Roditty, Seiferth, and Sharir…

This paper presents a new O(nlog(n)) algorithm for computing the convex hull of a set of 3 dimensional points. The algorithm first sorts the point in (x,y,z) then incrementally adds sorted points to the convex hull using the constraint that…

The 3D point cloud perception has emerged as a fundamental role for a wide range of applications. In particular, with the rapid development of neural networks, the voxel-based networks attract great attention due to their excellent…

We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic…

We study the convex hull membership (CHM) problem in the pure exploration setting where one aims to efficiently and accurately determine if a given point lies in the convex hull of means of a finite set of distributions. We give a complete…

The performance of particle advection-based flow visualization techniques is complex, since computational work can vary based on many factors, including number of particles, duration, and mesh type. Further, while many approaches have been…

This article describes a method to compute successive convex approximations of the convex hull of a set of points in R^n that are the solutions to a system of polynomial equations over the reals. The method relies on sums of squares of…

The spatial join is a popular operation in spatial database systems and its evaluation is a well-studied problem. As main memories become bigger and faster and commodity hardware supports parallel processing, there is a need to revamp…

When using the convex hull approach in the boundary modeling process, Model-Based Calibration (MBC) software suites -- such as Model-Based Calibration Toolbox from MathWorks -- can be computationally intensive depending on the amount of…

In this paper, we consider the polyhedral structure of the unit commitment polytope. In particular, we provide the convex hull results for the problem under the following different settings: 1) the convex hulls for the integrated…

Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…