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Maximum Rectilinear Crossing Number of Uniform Hypergraphs
We improve the lower bound on the d -dimensional rectilinear crossing number of the complete d -uniform hypergraph having 2 d vertices to
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Separating bichromatic point sets in the plane by restricted orientation convex hulls
We explore the separability of point sets in the plane by a restricted-orientation convex hull , which is an orientation-dependent, possibly...
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Sufficient Conditions for the Linear Convergence of an Algorithm for Finding the Metric Projection of a Point onto a Convex Compact Set
AbstractMany problems, for example, problems on the properties of the reachability set of a linear control system, are reduced to finding the...
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Rectilinear Crossings in Complete Balanced d-Partite d-Uniform Hypergraphs
In this paper, we study the embedding of a complete balanced d -partite d -uniform hypergraph with its nd vertices represented as points in general...
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A Convex Optimization Approach to Dynamic Programming in Continuous State and Action Spaces
In this paper, a convex optimization-based method is proposed for numerically solving dynamic programs in continuous state and action spaces. The key...
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Convexification techniques for linear complementarity constraints
We develop convexification techniques for mathematical programs with complementarity constraints. Specifically, we adapt the...
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An Object with a Striking Device and a Hostile Observer in Three-Dimensional Space
An autonomous object with a high-speed striking device is moving under observation, and a bodily observer has to hide from the device behind convex...
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Historical steps of development of convexity as a field
In this chapter we will show historical steps of the development of convexity as a field and, in addition, developments of the relations between...
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Convex Lifting-Type Methods for Curvature Regularization
Human visual perception is able to complete contours of objects even if they are disrupted or occluded in images. A possible mathematical imitation...
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On the generation of metric TSP instances with a large integrality gap by branch-and-cut
This paper introduces a computational method for generating metric Travelling Salesman Problem (TSP) instances having a large integrality gap. The...
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Minkowski Geometry—Some Concepts and Recent Developments
The geometry of finite-dimensional normed spaces (= Minkowski geometry) is a research topic which is related to many other fields, such as convex...
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Circle measurement
The problem with the circle is, that before measuring it, one has to prove that it has length, called perimeter). This appears difficult to...
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Tverberg’s Theorem, Disks, and Hamiltonian Cycles
For a finite set of S points in the plane and a graph with vertices on S , consider the disks with diameters induced by the edges. We show that for...
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A Simple Algorithm to Triangulate a Special Class of 3d Non-convex Polyhedra Without Steiner Points
We describe a simple algorithm to triangulate a special class of 3d non-convex polyhedra without Steiner points (vertices which are not the vertices...