Search

We propose a new relative-error inexact version of the alternating direction method of multipliers (ADMM) for convex optimization. We prove the asymptotic convergence of our main algorithm as well as pointwise and ergodic iteration-complexities for residuals. We also justify the effectiveness of the proposed algorithm through some preliminary numerical experiments on regression problems., Comment: To appear in Communications in Optimization Theory; 28 pages

In this work we apply the recently introduced framework of degenerate preconditioned proximal point algorithms to the hybrid proximal extragradient (HPE) method for maximal monotone inclusions. The latter is a method that allows inexact proximal (or resolvent) steps where the error is controlled by a relative-error criterion. Recently the HPE framework has been extended to the Douglas-Rachford method by Eckstein and Yao. In this paper we further extend the applicability of the HPE framework to splitting methods. To that end we use the framework of degenerate preconditioners that allows to write a large class of splitting methods as preconditioned proximal point algorithms. In this way we modify many splitting methods such that one or more of the resolvents can be computed inexactly with an error that is controlled by an adaptive criterion. Further, we illustrate the algorithmic framework in the case of Chambolle-Pock's primal dual hybrid gradient method and the Davis-Yin's forward Douglas-Rachford method. In both cases, the inexact computation of the resolvent shows clear advantages in computing time and accuracy., Comment: 33 pages, 6 figures

We propose an inertial variant of the strongly convergent inexact proximal-point (PP) method of Solodov and Svaiter (2000) for monotone inclusions. We prove strong convergence of our main algorithm under less restrictive assumptions on the inertial parameters when compared to previous analysis of inertial PP-type algorithms, which makes our method of interest even in finite-dimensional settings. We also performed an iteration-complexity analysis and applied our main algorithm to variational inequalities for monotone operators, obtaining strongly convergent (inertial) variants of Korpolevich's extragradient, forward-backward and Tseng's modified forward-backward methods.

We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from Monteiro and Svaiter (2012) by introducing a novel approach based on homotopy, which requires the resolution (at each iteration) of a single strongly monotone linear variational inequality. For a given tolerance $\rho>0$, our main algorithm exhibits pointwise $O\left(\frac{1}{\rho}\right)$ and ergodic $O\left(\frac{1}{\rho^{2/3}}\right)$ iteration-complexities. From a practical perspective, preliminary numerical experiments indicate that our main algorithm outperforms some previous proximal-Newton schemes.

Problems with the concordance cosmology $\Lambda$CDM as the cosmological constant problem, coincidence problems and Hubble tension has led to many proposed alternatives, as the $\Lambda(t)$CDM, where the now called $\Lambda$ cosmological term is allowed to vary due to an interaction with pressureless matter. Here, we analyze one class of these proposals, namely, $\Lambda=\alpha'a^{-2}+\beta H^2+\lambda_*$, based on dimensional arguments. Using SNe Ia, cosmic chronometers data plus constraints on $H_0$ from SH0ES and Planck satellite, we constrain the free parameters of this class of models. By using the Planck prior over $H_0$, we conclude that the $\lambda_*$ term can not be discarded by this analysis, thereby disfavouring models only with the time-variable terms. The SH0ES prior over $H_0$ has an weak evidence in this direction. The subclasses of models with $\alpha'=0$ and with $\beta=0$ can not be discarded by this analysis. Finally, by using distance priors from CMB, the $\Lambda$ time-dependence was quite restricted., Comment: Some references have been added and some have been corrected

This paper is devoted to the study of the spectral properties of the Weyl-Dirac or massless Dirac operators, describing the behavior of quantum quasi-particles in dimension 2 in a homogeneous magnetic field, $B^{\rm ext}$, perturbed by a chiral-magnetic field, $b^{\rm ind}$, with decay at infinity and a short-range scalar electric potential, $V$, of the Bessel-Macdonald type. These operators emerge from the action of a pristine graphene-like QED$_3$ model recently proposed in Eur. Phys. J. B93} (2020) 187. First, we establish the existence of states in the discrete spectrum of the Weyl-Dirac operators between the zeroth and the first (degenerate) Landau level assuming that $V=0$. In sequence, with $V_s \not= 0$, where $V_s$ is an attractive potential associated with the $s$-wave, which emerges when analyzing the $s$- and $p$-wave M{\o}ller scattering potentials among the charge carriers in the pristine graphene-like QED$_3$ model, we provide lower bounds for the sum of the negative eigenvalues of the operators $|\boldsymbol{\sigma} \cdot \boldsymbol{p}_{\boldsymbol{A}_\pm}|+ V_s$. Here, $\boldsymbol{\sigma}$ is the vector of Pauli matrices, $\boldsymbol{p}_{\boldsymbol{A}_\pm}=\boldsymbol{p}-\boldsymbol{A}_\pm$, with $\boldsymbol{p}=-i\boldsymbol{\nabla}$ the two-dimensional momentum operator and $\boldsymbol{A}_\pm$ certain magnetic vector potentials. As a by-product of this, we have the stability of bipolarons in graphene in the presence of magnetic fields., Comment: 23 pages, 2 figures

We address the question of the existence of bound states for a suitably projected two-dimensional massless Dirac operator in the presence of a Bessel-Macdonald potential (also known as $K_0$-potential potential), raised by De Lima, Del Cima and Miranda, in Eur.Phys.J. B (2020) 93, 187. Based on Relativistic Hardy Inequality, we prove that this operator has no bound states if $\gamma \leqslant \gamma_{\rm crit}$ (subcritical region), where $\gamma$ is a coupling constant., Comment: 8 pages. arXiv admin note: text overlap with arXiv:2005.08143

We propose and study the weak convergence of a projective splitting algorithm for solving multi-term composite monotone inclusion problems involving the finite sum of $n$ maximal monotone operators, each of which having an inner four-block structure: sum of maximal monotone, Lipschitz continuous, cocoercive and smooth differentiable operators. We show how to perform backward and half-forward steps with respect to the maximal monotone and Lipschitz$+$cocoercive components, respectively, while performing proximal-Newton steps with respect to smooth differentiable blocks., Comment: Some typos corrected; Accepted in Journal of Convex Analysis; 30 pages

For solving strongly convex optimization problems, we propose and study the global convergence of variants of the A-HPE and large-step A-HPE algorithms of Monteiro and Svaiter. We prove linear and the superlinear $\mathcal{O}\left(k^{\,-k\left(\frac{p-1}{p+1}\right)}\right)$ global rates for the proposed variants of the A-HPE and large-step A-HPE methods, respectively. The parameter $p\geq 2$ appears in the (high-order) large-step condition of the new large-step A-HPE algorithm. We apply our results to high-order tensor methods, obtaning a new inexact (relative-error) tensor method for (smooth) strongly convex optimization with iteration-complexity $\mathcal{O}\left(k^{\,-k\left(\frac{p-1}{p+1}\right)}\right)$. In particular, for $p=2$, we obtain an inexact Newton-proximal algorithm with fast global $\mathcal{O}\left(k^{\,-k/3}\right)$ convergence rate., Comment: minor corrections; to appear in optimization methods and software

Two methods of level set type are proposed for solving the Cauchy problem for an elliptic equation. Convergence and stability results for both methods are proven, characterizing the iterative methods as regularization methods for this ill-posed problem. Some numerical experiments are presented, showing the efficiency of our approaches and verifying the convergence results., Comment: 22 pages, 7 figures

In this paper, we propose a level set regularization approach combined with a split strategy for the simultaneous identification of piecewise constant diffusion and absorption coefficients from a finite set of optical tomography data (Neumann-to-Dirichlet data). This problem is a high nonlinear inverse problem combining together the exponential and mildly ill-posedness of diffusion and absorption coefficients, respectively. We prove that the parameter-to-measurement map satisfies sufficient conditions (continuity in the $L^1$ topology) to guarantee regularization properties of the proposed level set approach. On the other hand, numerical tests considering different configurations bring new ideas on how to propose a convergent split strategy for the simultaneous identification of the coefficients. The behavior and performance of the proposed numerical strategy is illustrated with some numerical examples., Comment: 25 pages, 7 figures

The Brown-Ravenhall operator was initially proposed as an alternative to describe the fermion-fermion interaction via Coulomb potential and subject to relativity. This operator is defined in terms of the associated Dirac operator and the projection onto the positive spectral subspace of the free Dirac operator. In this paper, we propose to analyze a modified version of the Brown-Ravenhall operator in two-dimensions. More specifically, we consider the Brown-Ravenhall operator with a short-range attractive potential given by a Bessel-Macdonald function (also known as $K_0$-potential) using the Foldy-Wouthuysen unitary transformation. Initially, we prove that the two-dimensional Brown-Ravenhall operator with $K_0$-potential is bounded from below when the coupling constant is below a specified critical value (a property also referred to as stability). A major feature of this model is the fact that it does not cease to be bounded below even if the coupling constant is above the specified critical value. We also investigate the nature of the spectrum of this operator, in particular the location of the essential spectrum, and the existence of eigenvalues, which are either isolated from the essential spectrum or embedded in it., Comment: 24 pages

This work addresses the conjugate heat transfer of a simplified PTT fluid flowing past an unbounded sphere in the Stokes regime ($Re = 0.01$). The problem is numerically solved with the finite-volume method assuming axial symmetry, absence of natural convection and constant physical properties. The sphere generates heat at a constant and uniform rate, and the analysis is conducted for a range of Deborah ($0 \leq De \leq 100$), Prandtl ($10^0 \leq Pr \leq 10^5$), Brinkman ($0 \leq Br \leq 100$) and conductivity ratios ($0.1 \leq \kappa \leq 10$), in the presence or absence of thermal contact resistance at the solid-fluid interface. The drag coefficient shows a monotonic decrease with $De$, whereas the stresses on the sphere surface and in the wake first increase and then decrease with $De$. A negative wake was observed for the two solvent viscosity ratios tested ($\beta$ = 0.1 and 0.5), being more intense for the more elastic fluid. In the absence of viscous dissipation, the average Nusselt number starts to decrease with $De$ after an initial increase. Heat transfer enhancement relative to an equivalent Newtonian fluid was observed for the whole range of conditions tested. The temperature of the sphere decreases and becomes more homogeneous when its thermal conductivity increases in relation to the conductivity of the fluid, although small changes are observed in the Nusselt number. The thermal contact resistance at the interface increases the average temperature of the sphere, without affecting significantly the shape of the temperature profiles inside the sphere. When viscous dissipation is considered, significant changes are observed in the heat transfer process as $Br$ increases. Overall, a simplified PTT fluid can enhance heat transfer compared to a Newtonian fluid, but increasing $De$ does not necessarily improve heat exchange.

Our view of the interstellar medium of the Milky Way and the universe beyond is affected by the structure of the local environment in the Solar neighborhood. Here, we present the discovery of a thirty-degree long arc of ultraviolet emission with a thickness of only a few arcminutes: the Ursa Major Arc. It consists of several arclets seen in the near- and far-ultraviolet bands of the GALEX satellite. A two-degree section of the arc was first detected in the H{\alpha} optical spectral line in 1997; additional sections were seen in the optical by the team of amateur astronomers included in this work. This direction of the sky is known for very low hydrogen column density and dust extinction; many deep fields for extra-galactic and cosmological investigations lie in this direction. Diffuse ultraviolet and optical interstellar emission are often attributed to scattering of light by interstellar dust. The lack of correlation between the Ursa Major Arc and thermal dust emission observed with the Planck satellite, however, suggests that other emission mechanisms must be at play. We discuss the origin of the Ursa Major Arc as the result of an interstellar shock in the Solar neighborhood., Comment: Accepted by A&A on April 3, 2020

For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits from a combination of inertial and relaxation effects, which are both controlled by parameters within a certain range. We propose sufficient conditions on these parameters and study the interplay between them in order to guarantee weak convergence of sequences generated by our algorithm. Additionally, the proposed algorithm also benefits from inexact subproblem solution within a relative-error criterion. Illustrative numerical experiments on LASSO problems indicate some improvement when compared with previous (noninertial and exact) versions of projective splitting., Comment: some typos corrected. Accepted for publication in Journal of Convex Analysis

This letter proposes a new approach to improve the accuracy of the Energy-based source localization methods in urban acoustic scenes. The proposed acoustic energy sensing flow estimation (ESFE) uses the sensors signal nonstationarity degree to determine the area with highest energy concentration in the scenes. The ESFE is applied to different acoustic scenes and yields to source localization accuracy improvement with computational complexity reduction. The experiments results show that the proposed scheme leads to significant improvement in source localization accuracy.

This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization. The analysis is based on a new inexact version of the proximal point algorithm that includes both an inertial step and overrelaxation. We apply our new inexact ADMM method to LASSO and logistic regression problems and obtain somewhat better computational performance than earlier inexact ADMM methods.

Faraday tomography allows us to map diffuse polarized synchrotron emission from our Galaxy and use it to interpret the magnetic field in the interstellar medium (ISM). We have applied Faraday tomography to 60 observations from the LOFAR Two-meter Sky Survey (LOTSS) and produced a Faraday depth cube mosaic covering 568 square degrees at high Galactic latitudes, at 4.3' angular resolution and 1 rad m$^{-2}$ Faraday depth resolution, with a typical noise level of 50--100 $\mu$Jy per point spread function (PSF) per rotation measure spread function (RMSF) (40-80 mK RMSF$^{-1}$). While parts of the images are strongly affected by instrumental polarization, we observe diffuse polarized emission throughout most of the field, with typical brightness between 1 and 6 K RMSF$^{-1}$, and Faraday depths between $-7$ and +25 rad m$^{-2}$. We observed many new polarization features, some up to 15 degrees in length. These include two regions with very uniformly structured, linear gradients in the Faraday depth; we measured the steepness of these gradients as 2.6 and 13 rad m$^{-2}$ deg$^{-1}$. We also observed a relationship between one of the gradients and an HI filament in the local ISM. Other ISM tracers were also checked for correlations with our polarization data and none were found, but very little signal was seen in most tracers in this region. We conclude that the LOTSS data are very well suited for Faraday tomography, and that a full-scale survey with all the LOTSS data has the potential to reveal many new Galactic polarization features and map out diffuse Faraday depth structure across the entire northern hemisphere., Comment: 23 pages, 16 figures, accepted by A&A. Figures have been degraded to comply with arXiv file size limits; full resolution figures will be available in the A&A version

We determined Faraday rotation measures (RMs) towards 137 pulsars in the northern sky, using Low-Frequency Array (LOFAR) observations at 110-190 MHz. This low-frequency RM catalogue, the largest to date, improves the precision of existing RM measurements on average by a factor of 20 - due to the low frequency and wide bandwidth of the data, aided by the RM synthesis method. We report RMs towards 25 pulsars for the first time. The RMs were corrected for ionospheric Faraday rotation to increase the accuracy of our catalogue to approximately 0.1 rad m$^{\rm -2}$. The ionospheric RM correction is currently the largest contributor to the measurement uncertainty. In addition, we find that the Faraday dispersion functions towards pulsars are extremely Faraday thin - mostly less than 0.001 rad m$^{\rm -2}$. We use these new precise RM measurements (in combination with existing RMs, dispersion measures, and distance estimates) to estimate the scale height of the Galactic halo magnetic field: 2.0$\pm$0.3 kpc for Galactic quadrants I and II above and below the Galactic plane (we also evaluate the scale height for these regions individually). Overall, our initial low-frequency catalogue provides valuable information about the 3-D structure of the Galactic magnetic field., Comment: 31 pages, including 13 figures, 6 tables. Accepted for publication in MNRAS

In this paper, we propose and study the asymptotic convergence and nonasymptotic global convergence rates (iteration-complexity) of an inertial under-relaxed version of the relative-error hybrid proximal extragradient (HPE) method for solving monotone inclusion problems. We analyze the proposed method under more flexible assumptions than existing ones on the extrapolation and relative-error parameters. As applications, we propose and/or study inertial under-relaxed forward-backward and Tseng's modified forward-backward type methods for solving structured monotone inclusions.