5,037 research outputs found
Finding largest small polygons with GloptiPoly
A small polygon is a convex polygon of unit diameter. We are interested in
small polygons which have the largest area for a given number of vertices .
Many instances are already solved in the literature, namely for all odd ,
and for and 8. Thus, for even , instances of this problem
remain open. Finding those largest small polygons can be formulated as
nonconvex quadratic programming problems which can challenge state-of-the-art
global optimization algorithms. We show that a recently developed technique for
global polynomial optimization, based on a semidefinite programming approach to
the generalized problem of moments and implemented in the public-domain Matlab
package GloptiPoly, can successfully find largest small polygons for and
. Therefore this significantly improves existing results in the domain.
When coupled with accurate convex conic solvers, GloptiPoly can provide
numerical guarantees of global optimality, as well as rigorous guarantees
relying on interval arithmetic
On the perimeters of simple polygons contained in a plane convex body
A simple n-gon is a polygon with n edges such that each vertex belongs to
exactly two edges and every other point belongs to at most one edge. Brass,
Moser and Pach asked the following question: For n > 3 odd, what is the maximum
perimeter of a simple n-gon contained in a Euclidean unit disk? In 2009, Audet,
Hansen and Messine answered this question, and showed that the supremum is the
perimeter of an isosceles triangle inscribed in the disk, with an edge of
multiplicity n-2. L\'angi generalized their result for polygons contained in a
hyperbolic disk. In this note we find the supremum of the perimeters of simple
n-gons contained in an arbitrary plane convex body in the Euclidean or in the
hyperbolic plane.Comment: 7 pages, 7 figure
On the perimeters of simple polygons contained in a disk
A simple -gon is a polygon with edges with each vertex belonging to
exactly two edges and every other point belonging to at most one edge. Brass
asked the following question: For odd, what is the maximum perimeter
of a simple -gon contained in a Euclidean unit disk?
In 2009, Audet, Hansen and Messine answered this question, and showed that
the optimal configuration is an isosceles triangle with a multiple edge,
inscribed in the disk. In this note we give a shorter and simpler proof of
their result, which we generalize also for hyperbolic disks, and for spherical
disks of sufficiently small radii.Comment: 6 pages, 2 figure
Health Care Opinion Leaders' Views on Delivery System Innovation and Improvement
Presents survey results on healthcare experts' views on strategies and models for fostering coordination and integration, such as accountable care systems, medical homes, and bundled payments; priorities among reform provisions; and market concerns
Pooling problem: Alternate formulations and solution methods
Copyright @ 2004 INFORMSThe pooling problem, which is fundamental to the petroleum industry, describes a situation in which products possessing different attribute qualities are mixed in a series of pools in such a way that the attribute qualities of the blended products of the end pools must satisfy given requirements. It is well known that the pooling problem can be modeled through bilinear and nonconvex quadratic programming. In this paper, we investigate how best to apply a new branch-and-cut quadratic programming algorithm to solve the pooling problem. To this effect, we consider two standard models: One is based primarily on flow variables, and the other relies on the proportion. of flows entering pools. A hybrid of these two models is proposed for general pooling problems. Comparison of the computational properties of flow and proportion models is made on several problem instances taken from the literature. Moreover, a simple alternating procedure and a variable neighborhood search heuristic are developed to solve large instances and compared with the well-known method of successive linear programming. Solution of difficult test problems from the literature is substantially accelerated, and larger ones are solved exactly or approximately.This project was funded by Ultramar Canada and Luc MassĂ©. The work of C. Audet was supported by NSERC (Natural Sciences and Engineering Research Council) fellowship PDF-207432-1998 and by CRPC (Center for Research on Parallel Computation). The work of J. Brimberg was supported by NSERC grant #OGP205041. The work of P. Hansen was supported by FCAR(Fonds pour la Formation des Chercheurs et lâAide Ă la Recherche)
grant #95ER1048, and NSERC grant #GP0105574
Navy-developed life support systems for fully enclosed protective suits
The development and performance of an environmental control unit capable of supporting a man in an impermeable suit at ambient temperatures up to 140 F for periods of up to two hrs is reported. The basic suit operation consists of cooling by wet ice contained in a suitcase. The system is designed to circulate and cool the air within the suit, to remove excess moisture and carbon dioxide, and to maintain a safe oxygen level
Serge Bouchard, Récits de Mathieu Mestokosho, chasseur innu. Préface de Gérard Bouchard. Montréal, Boréal, 2004, 192 p., photogr.
La dĂ©mocratie au pĂ©ril de lâĂ©conomie, sous la dir. de Marc Humbert et Alain CaillĂ©, Presses universitaires de Rennes, 2006, 367 p.
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