Related papers: Smallest Intersecting and Enclosing Balls
We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…
The aim of this paper is to establish a theory of Galerkin approximations to the space of convex and compact subsets of $\R^d$ with favorable properties, both from a theoretical and from a computational perspective. These Galerkin spaces…
The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space $\mathbb{R}^3$ are easier to feel by human's intuition. We give the maximum order of finite group actions on $(\mathbb{R}^3, \Sigma)$…
In this work we study the intersection properties of a finite disk system in the euclidean space. We accomplish this by utilizing subsets of spheres with varying dimensions and analyze specific points within them, referred to as poles.…
In this work, we prove that any two free boundary minimal hypersurfaces in the unit Euclidean ball have an intersection point in any half-ball. This is a strong version of the Frankel property proved by A. Fraser and M. Li \cite{FRLI}. As a…
In this paper, we study some optimization problems in uniformly convex and uniformly smooth Bochner spaces. We consider four cases of the underlying subsets: closed and convex subsets, closed and convex cones, closed subspaces and closed…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…
In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…
Counting Euclidean triangulations with vertices in a finite set $\C$ of the convex hull $\conv(\C)$ of $\C$ is difficult in general, both algorithmically and theoretically. The aim of this paper is to describe nearly convex polygons, a…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…
Evolutionary game theory studies populations that change in response to an underlying game. Often, the functional form relating outcome to player attributes or strategy is complex, preventing mathematical progress. In this work, we…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
Optimal packing of objects in containers is a critical problem in various real-life and industrial applications. This paper investigates the two-dimensional packing of convex polygons without rotations, where only translations are allowed.…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
An abstract indefinite least squares problem with a quadratic constraint is considered. This is a quadratic programming problem with one quadratic equality constraint, where neither the objective nor the constraint are convex functions.…
The convex hull cheapest insertion heuristic produces good solutions to the Euclidean Traveling Salesperson Problem, but it has never been extended to the non-Euclidean problem. This paper uses multidimensional scaling to first project the…
Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an…