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 $n$. Many instances are already solved in the literature, namely for all odd $n$, and for $n=4, 6$ and 8. Thus, for even $n\geq 10$, 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 $n=10$ and $n=12$. 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

Sharing Resources: Opportunities for Smaller Primary Care Practices to Increase Their Capacity for Patient Care

Outlines findings linking shared resources with use of health information technology, care coordination, self-management, and quality monitoring, and strategies to increase resources among small and midsize practices by expanding shared resource models

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 Massé. 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 l’Aide à la Recherche) grant #95ER1048, and NSERC grant #GP0105574

Optimization of laser-plasma injector via beam loading effects using ionization-induced injection

Simulations of ionization induced injection in a laser driven plasma wakefield show that high-quality electron injectors in the 50-200 MeV range can be achieved in a gas cell with a tailored density profile. Using the PIC code Warp with parameters close to existing experimental conditions, we show that the concentration of $\mathrm{N_2}$ in a hydrogen plasma with a tailored density profile is an efficient parameter to tune electron beam properties through the control of the interplay between beam loading effects and varying accelerating field in the density profile. For a given laser plasma configuration, with moderate normalized laser amplitude, $a_0=1.6$ and maximum electron plasma density, $n_{e0}=4\times 10^{18}\,\mathrm{cm^{-3}}$, the optimum concentration results in a robust configuration to generate electrons at 150~MeV with a rms energy spread of 4\% and a spectral charge density of 1.8~pC/MeV.Comment: 13 pages, 10 figure

Delivery System Reform Tracking: A Framework for Understanding Change

Proposes a framework for tracking progress on delivery system reforms such as patient-centered medical homes and accountable care organizations by assessing structures, capabilities, incentives, and outcomes. Outlines challenges for data collection

derivative-free nonlinear programming

algorithm with a progressive barrier fo

Parallel Space Decomposition of the Mesh Adaptive Direct Search Algorithm

This paper describes a Parallel Space Decomposition (PSD) technique for the Mesh Adaptive Direct Search (MADS) algorithm. MADS extends Generalized Pattern Search for constrained nonsmooth optimization problems. The objective here is to solve larger problems more efficiently. The new method (PSD-MADS) is an asynchronous parallel algorithm in which the processes solve problems over subsets of variables. The convergence analysis based on the Clarke calculus is essentially the same as for the MADS algorithm. A practical implementation is described and some numerical results on problems with up to 500 variables illustrate advantages and limitations of PSD-MADS

A Comparison Of Hip And Knee Joint Kinematics Between Two Alpine Ski Ergometers

This study was conducted to determine if hip and knee joint kinematics differed between conditions as subjects "skied" on two alpine ski ergometers. Eleven male recreational skiers, ages 18-23, participated in the study. During the random test, sagittal plane motions of the hip and knee joints were videotaped as subjects skied on each ski ergometer at a slow speed (92 turns/minute) and a fast speed (102 turns/minute). Each subject was vid.eotaped at 30 frames per second during the last thirty seconds of a two minute exercise bout. Three turns were randomly selected and digitized on the Ariel Performance Analysis System (APAS). Relative angular displacements of the left hip and knee were measured and compared. Hip and knee flexion were significantly different between the two ergometers at the fast speed. A comparison of the fast and slow trials revealed that subjects were able to achieve more knee flexion at the fast speed on one ergometer. However, on the other ergometer, the degree of knee flexion was greater at the slow speed. How closely the two ski ergometers simulate actual downhill skiing is unknown and warrants further investigation