Related papers: A QCQP Approach to Triangulation
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective…
In this paper, we propose a new easily implementable method for solving a class of semi-infinite programs, where an approximate linear semidefinite program is constructed for the concerned semi-infinite program based on the duality theory…
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Estimating the pose of a camera with respect to a 3D reconstruction or scene representation is a crucial step for many mixed reality and robotics applications. Given the vast amount of available data nowadays, many applications constrain…
We consider several problems that involve lines in three dimensions, and present improved algorithms for solving them. The problems include (i) ray shooting amid triangles in $R^3$, (ii) reporting intersections between query lines…
This paper presents a computationally-efficient method for evaluating the feasibility of Quadratic Programs (QPs) for online constrained control. Based on the duality principle, we first show that the feasibility of a QP can be determined…
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of…
Modeling parts of an optimization problem as an optimal value function that depends on a top-level decision variable is a regular occurrence in optimization and an essential ingredient for methods such as Benders Decomposition. It often…
Two new algorithms are described for matching two dimensional coordinate lists of point sources that are signifcantly faster than previous methods. By matching rarely occurring triangles (or more complex shapes) in the two lists, and by…
Mixed-Integer Quadratic Programming (MIQP) has been identified as a suitable approach for finding an optimal solution to the behavior planning problem with low runtimes. Logical constraints and continuous equations are optimized alongside.…
Supervised approaches to 3D pose estimation from single images are remarkably effective when labeled data is abundant. However, as the acquisition of ground-truth 3D labels is labor intensive and time consuming, recent attention has shifted…
Let $P$ and $Q$ be two simple polygons in the plane of total complexity $n$, each of which can be decomposed into at most $k$ convex parts. We present an $(1-\varepsilon)$-approximation algorithm, for finding the translation of $Q$, which…
We consider the problem of approximating a truncated Gaussian kernel using Fourier (trigonometric) functions. The computation-intensive bilateral filter can be expressed using fast convolutions by applying such an approximation to its range…
Symmetry is the essential element of lifted inference that has recently demon- strated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models models. This raises the question, whether…
Let $P$ and $Q$ be polytopes, the first of "low" dimension and the second of "high" dimension. We show how to triangulate the product $P \times Q$ efficiently (i.e., with few simplices) starting with a given triangulation of $Q$. Our method…
For nonconvex quadratically constrained quadratic programs (QCQPs), we first show that, under certain feasibility conditions, the standard semidefinite (SDP) relaxation is exact for QCQPs with bipartite graph structures. The exact optimal…
This paper proves that non-convex quadratically constrained quadratic programs can be solved in polynomial time when their underlying graph is acyclic, provided the constraints satisfy a certain technical condition. When this condition is…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…