An optimal-basis identification technique for interior-point linear programming algorithms

AbstractThis work concerns a method for identifying an optimal basis for linear programming problems in the setting of interior-point methods. To each iterate xk generated by a primal interior-point algorithm, say, we associate an indicator vector qk with the property that if xk converges to a nondegenerate vertex x∗, then qk converges to the 0–1 vector sign(x∗). More interestingly, we show that the convergence of qk is quadratically faster than that of xk in the sense that ||qk−q7ast;||=O(||xk−x∗||2). This clear-cut separation and rapid convergence allow one to infer at an intermediate stage of the iterative process which variables will be zero at optimality and which will not. We also show that under suitable assumptions this method is applicable to dual as well as primal-dual algorithms and can be extended to handle certain types of degeneracy. Numerical examples are included to corroborate the convergence properties of the indicators. The practical limitations of the indicator technique are also discussed

On the Convergence of the Mizuno-Todd-Ye Algorithm to the Analytic Center of the Solution Set

In this work we demonstrate that the Mizuno-Todd-Ye predictor corrector primal-dual interior-point method for linear programming generates iteration sequences that converge to the analytic center of the solution set

Sizing the BFGS and DFP Updates: A Numerical Study

In this study we develop and test a strategy for selectively sizing (multiplying by an appropriate scalar) the approximate Hessian matrix before it is updated in the BFGS and DFP trust-region methods for unconstrained optimization. Our numerical results imply that for use with the DFP update the Oren-Luenberger sizing factor is completely satisfactory and selective sizing is vastly superior to the alternatives of never sizing, or first-iteration sizing, and is slightly better than the alternative of always sizing. Numerical experimentation showed that the Oren-Luenberger sizing factor is not a satisfactory sizing factor for use with the BFGS update. Therefore, based on our newly acquired understanding of the situation, we propose a damped Oren-Luenberger sizing factor to be used with the BFGS update. Our numerical experimentation implies that selectively sizing the BFGS update with the damped Oren-Luenberger sizing factor is superior to the alternatives. These results contradict the folk-axiom that sizing should be done only at the first iteration. They also show that without sufficient sizing, DFP is vastly inferior to BFGS; however, when selectively sized, DFP is competitive with BFGS

Comportamiento ecológico ciudadano: un análisis crítico desde la corriente del pensamiento ambiental latinoamericano

El objetivo del artículo es realizar una valoración crítica del comportamiento ecológico del ciudadano latinoamericano a partir de la influencia de las corrientes filosóficas del pensamiento ambiental en la región, para ello, se usó como metodología el análisis hermenéutico de obras de grandes pensadores de la región, como Boff (1997, 2012, 2015), Maya (2003, 2008), Rozzi (2001, 2007, 2012), Leff (2010, 2011, 2020), entre otros. Se pudo determinar que la conducta ecológica ciudadana ha estado regida por las directrices del sistema político imperante, basado en el principio único de explotación de recursos naturales para obtener beneficios económicos, dejando de un lado el pensamiento ecocéntrico, se espera, que el reciente acuerdo de Escazú y la influencia ejercida de pensadores ecológicos modele el comportamiento social, partiendo de la democratización de la información ambiental, creación de bases jurídicas sostenibles y la participación organizada del ciudadano.Campus Lima Centr

The exposure of the hybrid detector of the Pierre Auger Observatory

The Pierre Auger Observatory is a detector for ultra-high energy cosmic rays. It consists of a surface array to measure secondary particles at ground level and a fluorescence detector to measure the development of air showers in the atmosphere above the array. The "hybrid" detection mode combines the information from the two subsystems. We describe the determination of the hybrid exposure for events observed by the fluorescence telescopes in coincidence with at least one water-Cherenkov detector of the surface array. A detailed knowledge of the time dependence of the detection operations is crucial for an accurate evaluation of the exposure. We discuss the relevance of monitoring data collected during operations, such as the status of the fluorescence detector, background light and atmospheric conditions, that are used in both simulation and reconstruction.Comment: Paper accepted by Astroparticle Physic

Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems

The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces

Evidence for a mixed mass composition at the `ankle' in the cosmic-ray spectrum

We report a first measurement for ultra-high energy cosmic rays of the correlation between the depth of shower maximum and the signal in the water Cherenkov stations of air-showers registered simultaneously by the fluorescence and the surface detectors of the Pierre Auger Observatory. Such a correlation measurement is a unique feature of a hybrid air-shower observatory with sensitivity to both the electromagnetic and muonic components. It allows an accurate determination of the spread of primary masses in the cosmic-ray flux. Up till now, constraints on the spread of primary masses have been dominated by systematic uncertainties. The present correlation measurement is not affected by systematics in the measurement of the depth of shower maximum or the signal in the water Cherenkov stations. The analysis relies on general characteristics of air showers and is thus robust also with respect to uncertainties in hadronic event generators. The observed correlation in the energy range around the `ankle' at $\lg(E/{\rm eV})=18.5-19.0$ differs significantly from expectations for pure primary cosmic-ray compositions. A light composition made up of proton and helium only is equally inconsistent with observations. The data are explained well by a mixed composition including nuclei with mass $A > 4$. Scenarios such as the proton dip model, with almost pure compositions, are thus disfavoured as the sole explanation of the ultrahigh-energy cosmic-ray flux at Earth.Comment: Published version. Added journal reference and DOI. Added Report Numbe

Strange particle production in proton-proton collisions at s=0.9\sqrt{s}=0.9 TeV with ALICE at the LHC

The production of mesons containing strange quarks (K$^0_s$, $\phi$) and both singly and doubly strange baryons ($\Lambda$, Anti-$\Lambda$, and $\Xi$+Anti-$\Xi$) are measured at central rapidity in pp collisions at $\sqrt{s}$ = 0.9 TeV with the ALICE experiment at the LHC. The results are obtained from the analysis of about 250 k minimum bias events recorded in 2009. Measurements of yields (dN/dy) and transverse momentum spectra at central rapidities for inelastic pp collisions are presented. For mesons, we report yields () of 0.184 $\pm$ 0.002 stat. $\pm$ 0.006 syst. for K$^0_s$ and 0.021 $\pm$ 0.004 stat. $\pm$ 0.003 syst. for $\phi$. For baryons, we find = 0.048 $\pm$ 0.001 stat. $\pm$ 0.004 syst. for $\Lambda$, 0.047 $\pm$ 0.002 stat. $\pm$ 0.005 syst. for Anti-$\Lambda$ and 0.0101 $\pm$ 0.0020 stat. $\pm$ 0.0009 syst. for $\Xi$+Anti-$\Xi$. The results are also compared with predictions for identified particle spectra from QCD-inspired models and provide a baseline for comparisons with both future pp measurements at higher energies and heavy-ion collisions.Comment: 33 pages, 21 captioned figures, 10 tables, authors from page 28, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/387

Anisotropic flow of charged hadrons, pions and (anti-)protons measured at high transverse momentum in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}}=2.76 TeV

The elliptic, $v_2$, triangular, $v_3$, and quadrangular, $v_4$, azimuthal anisotropic flow coefficients are measured for unidentified charged particles, pions and (anti-)protons in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV with the ALICE detector at the Large Hadron Collider. Results obtained with the event plane and four-particle cumulant methods are reported for the pseudo-rapidity range $|\eta|<0.8$ at different collision centralities and as a function of transverse momentum, $p_{\rm T}$, out to $p_{\rm T}=20$ GeV/$c$. The observed non-zero elliptic and triangular flow depends only weakly on transverse momentum for $p_{\rm T}>8$ GeV/$c$. The small $p_{\rm T}$ dependence of the difference between elliptic flow results obtained from the event plane and four-particle cumulant methods suggests a common origin of flow fluctuations up to $p_{\rm T}=8$ GeV/$c$. The magnitude of the (anti-)proton elliptic and triangular flow is larger than that of pions out to at least $p_{\rm T}=8$ GeV/$c$ indicating that the particle type dependence persists out to high $p_{\rm T}$.Comment: 16 pages, 5 captioned figures, authors from page 11, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/186

Centrality dependence of charged particle production at large transverse momentum in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm{NN}}} = 2.76 TeV

The inclusive transverse momentum ($p_{\rm T}$) distributions of primary charged particles are measured in the pseudo-rapidity range $|\eta|<0.8$ as a function of event centrality in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}=2.76$ TeV with ALICE at the LHC. The data are presented in the $p_{\rm T}$ range $0.15<p_{\rm T}<50$ GeV/$c$ for nine centrality intervals from 70-80% to 0-5%. The Pb-Pb spectra are presented in terms of the nuclear modification factor $R_{\rm{AA}}$ using a pp reference spectrum measured at the same collision energy. We observe that the suppression of high-$p_{\rm T}$ particles strongly depends on event centrality. In central collisions (0-5%) the yield is most suppressed with $R_{\rm{AA}}\approx0.13$ at $p_{\rm T}=6$-7 GeV/$c$. Above $p_{\rm T}=7$ GeV/$c$, there is a significant rise in the nuclear modification factor, which reaches $R_{\rm{AA}} \approx0.4$ for $p_{\rm T}>30$ GeV/$c$. In peripheral collisions (70-80%), the suppression is weaker with $R_{\rm{AA}} \approx 0.7$ almost independently of $p_{\rm T}$. The measured nuclear modification factors are compared to other measurements and model calculations.Comment: 17 pages, 4 captioned figures, 2 tables, authors from page 12, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/284