GMRES-Accelerated ADMM for Quadratic Objectives

We consider the sequence acceleration problem for the alternating direction method-of-multipliers (ADMM) applied to a class of equality-constrained problems with strongly convex quadratic objectives, which frequently arise as the Newton subproblem of interior-point methods. Within this context, the ADMM update equations are linear, the iterates are confined within a Krylov subspace, and the General Minimum RESidual (GMRES) algorithm is optimal in its ability to accelerate convergence. The basic ADMM method solves a $\kappa$-conditioned problem in $O(\sqrt{\kappa})$ iterations. We give theoretical justification and numerical evidence that the GMRES-accelerated variant consistently solves the same problem in $O(\kappa^{1/4})$ iterations for an order-of-magnitude reduction in iterations, despite a worst-case bound of $O(\sqrt{\kappa})$ iterations. The method is shown to be competitive against standard preconditioned Krylov subspace methods for saddle-point problems. The method is embedded within SeDuMi, a popular open-source solver for conic optimization written in MATLAB, and used to solve many large-scale semidefinite programs with error that decreases like $O(1/k^{2})$, instead of $O(1/k)$, where $k$ is the iteration index.Comment: 31 pages, 7 figures. Accepted for publication in SIAM Journal on Optimization (SIOPT

Wind-turbine wake encounter by light aircraft

No abstract available

Antenna array optimisation using semidefinite programming for cellular communications from HAPs

Array pattern optimisation based on semidefinite programming (SDP) is proposed to improve the coverage performance of cellular communications from High Altitude Platforms (HAPs). This optimisation, when applied to a linear vertical array of N omnidirectional antenna elements, allows a coverage performance better than that of an array of N narrowbeam aperture antennas forming hexagonal cells on the ground. In addition to the performance enhancement, the HAP antenna payload can be significantly reduced

On the Nagaoka polaron in the t-J model

It is widely believed that a single hole in the two (or three) dimensional t-J model, for sufficiently small exchange coupling J, creates a ferromagnetic bubble around itself, a finite J remnant of the ferromagnetic groundstate at J=0 (the infinite U Hubbard model), first established by Nagaoka. We investigate this phenomenon in two dimensions using the density matrix renormalization group, for system sizes up to 9x9. We find that the polaron forms for J/t<0.02-0.03 (a somewhat larger value than estimated previously). Although finite-size effects appear large, our data seems consistent with the expected 1.1(J/t)^{-1/4} variation of polarion radius. We also test the Brinkman-Rice model of non-retracing paths in a Neel background, showing that it is quite accurate, at larger J. Results are also presented in the case where the Heisenberg interaction is dropped (the t-J^z model). Finally we discuss a "dressed polaron" picture in which the hole propagates freely inside a finite region but makes only self-retracing excursions outside this region.Comment: 7 pages, 9 encapsulated figure

Deconvolution of ASCA X-ray data: II. Radial temperature and metallicity profiles for 106 galaxy clusters

In Paper-I we presented a methodology to recover the spatial variations of properties of the intracluster gas from ASCA X-ray satellite observations of galaxy clusters. We verified the correctness of this procedure by applying it to simulated cluster datasets which we had subjected to the various contaminants common in ASCA data. In this paper we present the results which we obtain when we apply this method to real galaxy cluster observations. We determine broad-band temperature and cooling-flow mass-deposition rates for the 106 clusters in our sample, and obtain temperature, abundance and emissivity profiles (i.e. at least two annular bins) for 98 of these clusters. We find that 90 percent of these temperature profiles are consistent with isothermality at the 3-sigma confidence level. This conflicts with the prevalence of steeply-declining cluster temperature profiles found by Markevitch et al. (1998) from a sample of 30 clusters. In Paper-III (in preparation) we utilise our temperature and emissivity profiles to determine radial hydrostatic-mass properties for a subsample of the clusters presented in this paper.Comment: MNRAS, accpeted. Postscript copy of paper and individual postscript files for plots in Appendix B can be obtained from: http://www-xray.ast.cam.ac.uk/~da

Quasiballistic correction to the density of states in three-dimensional metal

We study the exchange correction to the density of states in the three-dimensional metal near the Fermi energy. In the ballistic limit, when the distance to the Fermi level exceeds the inverse transport relaxation time $1/\tau$, we find the correction linear in the distance from the Fermi level. By a large parameter $\epsilon_{\rm F} \tau$ this ballistic correction exceeds the diffusive correction obtained earlier.Comment: 2 pages, 1 figur

A Prediction of Observable Rotation in the ICM of Abell 3266

We present a numerical Hydro+N-body model of A3266 whose X-ray surface brightness, temperature distribution, and galaxy spatial and velocity distribution data are consistent with the A3266 data. The model is an old (~3 Gyr), off-axis merger having a mass ratio of ~2.5:1. The less massive subcluster in the model is moving on a trajectory from southwest to northeast passing on the western side of the dominant cluster while moving into the plane of the sky at ~45 degrees. Off-axis mergers such as this one are an effective mechanism for transferring angular momentum to the intracluster medium (ICM), making possible a large scale rotation of the ICM. We demonstrate here that the ICM rotation predicted by our fully 3-dimensional model of A3266 is observable with current technology. As an example, we present simulated observations assuming the capabilities of the high resolution X-ray spectrometer (XRS) which was to have flown on Astro-E.Comment: 9 pages, 7 postscript figures, Fig. 3 and 6 are color postscript, Accepted for publication in the Astrophysical Journa

A Two-dimensional Infinte System Density Matrix Renormalization Group Algorithm

It has proved difficult to extend the density matrix renormalization group technique to large two-dimensional systems. In this Communication I present a novel approach where the calculation is done directly in two dimensions. This makes it possible to use an infinite system method, and for the first time the fixed point in two dimensions is studied. By analyzing several related blocking schemes I find that there exists an algorithm for which the local energy decreases monotonically as the system size increases, thereby showing the potential feasibility of this method.Comment: 5 pages, 6 figure