Related papers: Visible Points in Convex Sets and Best Approximati…
The farthest point map sends a point in a compact metric space to the set of points farthest from it. We focus on the case when this metric space is a convex centrally symmetric polyhedron, so that we can compose the farthest point map with…
In this note, we highlight some properties of the metric projection onto a closed convex in a Hilbert space. In particular, we use some recent results on fixed points of nonexpansive potential operators.
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…
We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks implicitly represent both the support and gauge functions of a convex body. We prove a universal…
We prove that for any compact set B in R^d and for any epsilon >0 there is a finite subset X of B of |X|=d^{O(1/epsilon^2)} points such that the maximum absolute value of any linear function ell: R^d --> R on X approximates the maximum…
In this paper the problem of maximizing the distance to a given fixed point over an intersection of balls is considered. It is known that this problem is NP complete in the general case, since any subset sum problem can be solved upon…
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…
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…
Accurate localization in diverse environments is a fundamental challenge in computer vision and robotics. The task involves determining a sensor's precise position and orientation, typically a camera, within a given space. Traditional…
Points of interest on a map such as restaurants, hotels, or subway stations, give rise to categorical point data: data that have a fixed location and one or more categorical attributes. Consequently, recent years have seen various set…
The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…
The notion of ball convexity, considered in finite dimensional real Banach spaces, is a natural and useful extension of usual convexity; one replaces intersections of half-spaces by suitable intersections of balls. A subset $S$ of a normed…
Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is…
We establish an approximate fixed point result for self-maps on compact convex subsets of Hausdorff topological vector spaces where continuity is not a necessary condition.
A new notion of face relative interior for convex sets in topological real vector spaces is introduced in this work. Face relative interior is grounded in the facial structure, and may capture the geometry of convex sets in topological…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
The projection onto the intersection of sets generally does not allow for a closed form even when the individual projection operators have explicit descriptions. In this work, we systematically analyze the projection onto the intersection…
We consider the problem of mirror invisibility for plane sets. Given a circle and a finite number of unit vectors (defining the directions of invisibility) such that the angles between them are commensurable with $\pi$, for any $\varepsilon…
We introduce an asymptotic notion of positivity in algebraic geometry that turns out to be related to some high-dimensional convex sets. The dimension of the convex sets grows with the number of birational operations. In the case of complex…
Inspired by the finding that vanishing point (road tangent) guides driver's gaze, in our previous work we showed that vanishing point attracts gaze during free viewing of natural scenes as well as in visual search (Borji et al., Journal of…