Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections

This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and an efficient preconditioning strategy is crucial for the efficiency of the overall method. Constraint preconditioners are very effective in this context; nevertheless, their computation may be very expensive for large-scale problems, and resorting to approximations of them may be convenient. Here we propose a procedure for building inexact constraint preconditioners by updating a "seed" constraint preconditioner computed for a KKT matrix at a previous interior point iteration. These updates are obtained through low-rank corrections of the Schur complement of the (1,1) block of the seed preconditioner. The updated preconditioners are analyzed both theoretically and computationally. The results obtained show that our updating procedure, coupled with an adaptive strategy for determining whether to reinitialize or update the preconditioner, can enhance the performance of interior point methods on large problems.Comment: 22 page

The GASMEMS network: Rationale, programme and initial results

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.GASMEMS is an Initial Training Network supported by the European Commission, which aims at training young researchers in the field of rarefied gas flows in MEMS, and at structuring research in Europe in the field of gas microflows in order to improve global fundamental knowledge and enable technological applications to an industrial and commercial level. The partners and the global objectives of this 4 year programme are detailed, and some initial results are presented. First experimental data about the flow of binary gas mixtures through rectangular microchannels are successfully compared with continuum and kinetic models, in the slip flow and early transition regimes. The behaviour of these mixtures has also been simulated in triangular microchannels, for the whole range of the Knudsen number, using a kinetic approach and the McCormack model. Heat transfer in plane microchannels has been numerically investigated, pointing out compressibility and rarefaction effects. The effect of thermal creep has been studied comparing BGK, Smodel and ellipsoidal model with the solution from the full Boltzmann equation. A semi-analytical model of the Knudsen layer has been developed and used to simulate the problem of thermal transpiration in a microchannel. Gaseous flows through rough microchannels have been simulated using kinetic theory and DSMC method, the wall roughness being simulated as a highly porous medium of variable thickness.This study is funded by the European Community's Seventh Framework Programme FP7/2007-2013 under grant agreement ITN GASMEMS n° 215504

Association between diverticulosis and colonic neoplastic lesions in individuals with a positive faecal immunochemical test

Background The association between diverticulosis and colonic neoplastic lesions has been suggested, but data in literature are conflicting. This study aimed to investigate such a relationship in patients participating in a colorectal cancer screening program who underwent high-quality colonoscopy.Methods Data from consecutive individuals 50-75 years of age with a positive faecal immunological test were considered. Diverticulosis was categorised as present or absent. The prevalence of neoplastic lesions (adenoma, advanced adenoma, and cancer) between individuals with and those without diverticula was compared. A multivariate analysis was performed.Results Overall, data from 970 consecutive individuals were evaluated, and diverticulosis was detected in 354 (36.5%) cases. At least one adenoma was detected in 490 (50.5%) people, at least one advanced adenoma in 264 (27.2%), multiple adenoma in 71 (7.3%), whilst a cancer was diagnosed in 48 (4.9%) cases. At univariate analysis, the adenoma detection rate in patients with diverticula was significantly higher than in controls (55.9% vs 47.4%; p=0.011). At multivariate analysis, presence of diverticulosis was an independent risk factor for both adenoma detection rate (OR=1.58; 95% CI=1.14-2.18; p=0.006) and advanced adenoma (OR=1.57; 95% CI=1.10-2.24; p=0.013), but not for colorectal cancer.Conclusions In a colorectal screening setting, the adenoma detection rate was significantly higher in individuals with diverticulosis than in controls

A Non-Local Mean Curvature Flow and its semi-implicit time-discrete approximation

We address in this paper the study of a geometric evolution, corresponding to a curvature which is non-local and singular at the origin. The curvature represents the first variation of the energy recently proposed as a variant of the standard perimeter penalization for the denoising of nonsmooth curves. To deal with such degeneracies, we first give an abstract existence and uniqueness result for viscosity solutions of non-local degenerate Hamiltonians, satisfying suitable continuity assumption with respect to Kuratowsky convergence of the level sets. This abstract setting applies to an approximated flow. Then, by the method of minimizing movements, we also build an "exact" curvature flow, and we illustrate some examples, comparing the results with the standard mean curvature flow

An optimally fast objective-function-free minimization algorithm using random subspaces

An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this random approximation technique does not affect the method's convergence nor its evaluation complexity for the search of an $\epsilon$-approximate first-order critical point, which is $\mathcal{O}(\epsilon^{-(p+1)/p})$, where $p$ is the order of derivatives used. A variant of the algorithm using approximate Hessian matrices is also analyzed and shown to require at most $\mathcal{O}(\epsilon^{-2})$ evaluations. Preliminary numerical tests show that the random-subspace technique can significantly improve performance on some problems, albeit, unsurprisingly, not for all.Comment: 23 page

Experimental measurements of thermal-hydraulic performance of aluminum-foam water-to-air heat exchangers for a HVAC application

In this paper, thermal and hydraulic performance of in-house made prototypes of water-to-air heat exchangers are experimentally investigated and compared to those of a compact heat exchanger, used in a commercial fan coil. The prototypes are built replacing the fins with aluminum foam surfaces characterized by a large porosity, higher than 96%. In order to evaluate the performance of the foam-based heat exchangers in a real-scale application, the geometry of the prototypes was based on that of the reference model and, moreover, experimental tests were performed placing the heat exchangers within the commercial cabinet, under the same fan power. Different bonding techniques were also tested to couple metal foams to copper tubes. Results show that similar hydraulic performance can be obtained with the foam-based heat exchangers, if compared to the commercial device. However, the large foam porosity accounts for a lower value of the surface-to-volume ratio of the aluminum foam media, thus yielding a strong penalty, up to 60%, of the heat transfer rate with respect to that of the conventional finned surface. Moreover, experimental results highlight how the bonding technique and the foam packaging have a strong influence on the contact thermal resistance and, consequently, on the overall heat transfer coefficient. Epoxy bonding allows to increase the thermal performance of the heat exchanger, if compared to press fitting, between 15% and 110%. In conclusion, results presented in this paper suggest that metal foams can be considered as a potential alternative to fins in water-to-air heat exchangers only if the foam tube bonding is obtained by welding or brazing