A two-phase gradient method for quadratic programming problems with a single linear constraint and bounds on the variables

We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G. Toraldo, SIAM J. Optim. 1, 1991], our approach alternates between two phases until convergence: an identification phase, which performs gradient projection iterations until either a candidate active set is identified or no reasonable progress is made, and an unconstrained minimization phase, which reduces the objective function in a suitable space defined by the identification phase, by applying either the conjugate gradient method or a recently proposed spectral gradient method. However, the algorithm differs from GPCG not only because it deals with a more general class of problems, but mainly for the way it stops the minimization phase. This is based on a comparison between a measure of optimality in the reduced space and a measure of bindingness of the variables that are on the bounds, defined by extending the concept of proportioning, which was proposed by some authors for box-constrained problems. If the objective function is bounded, the algorithm converges to a stationary point thanks to a suitable application of the gradient projection method in the identification phase. For strictly convex problems, the algorithm converges to the optimal solution in a finite number of steps even in case of degeneracy. Extensive numerical experiments show the effectiveness of the proposed approach.Comment: 30 pages, 17 figure

Directional TGV-based image restoration under Poisson noise

We are interested in the restoration of noisy and blurry images where the texture mainly follows a single direction (i.e., directional images). Problems of this type arise, for example, in microscopy or computed tomography for carbon or glass fibres. In order to deal with these problems, the Directional Total Generalized Variation (DTGV) was developed by Kongskov et al. in 2017 and 2019, in the case of impulse and Gaussian noise. In this article we focus on images corrupted by Poisson noise, extending the DTGV regularization to image restoration models where the data fitting term is the generalized Kullback-Leibler divergence. We also propose a technique for the identification of the main texture direction, which improves upon the techniques used in the aforementioned work about DTGV. We solve the problem by an ADMM algorithm with proven convergence and subproblems that can be solved exactly at a low computational cost. Numerical results on both phantom and real images demonstrate the effectiveness of our approach.Comment: 20 pages, 1 table, 13 figure

Using gradient directions to get global convergence of Newton-type methods

The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [IMA Journal of Numerical Analysis, 8 (1988)] has driven us to consider a globalization strategy based on SD, which is applicable to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. Scaling the SD directions with a suitable step length makes a significant difference with respect to similar globalization approaches, in terms of both theoretical features and computational behavior. We apply our strategy to Newton's method and the BFGS method, with computational results that appear interesting compared with the results of well-established globalization strategies devised ad hoc for those methods.Comment: 22 pages, 11 Figure

ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration

We propose a method, called ACQUIRE, for the solution of constrained optimization problems modeling the restoration of images corrupted by Poisson noise. The objective function is the sum of a generalized Kullback-Leibler divergence term and a TV regularizer, subject to nonnegativity and possibly other constraints, such as flux conservation. ACQUIRE is a line-search method that considers a smoothed version of TV, based on a Huber-like function, and computes the search directions by minimizing quadratic approximations of the problem, built by exploiting some second-order information. A classical second-order Taylor approximation is used for the Kullback-Leibler term and an iteratively reweighted norm approach for the smoothed TV term. We prove that the sequence generated by the method has a subsequence converging to a minimizer of the smoothed problem and any limit point is a minimizer. Furthermore, if the problem is strictly convex, the whole sequence is convergent. We note that convergence is achieved without requiring the exact minimization of the quadratic subproblems; low accuracy in this minimization can be used in practice, as shown by numerical results. Experiments on reference test problems show that our method is competitive with well-established methods for TV-based Poisson image restoration, in terms of both computational efficiency and image quality.Comment: 37 pages, 13 figure

LSOS: Line-search Second-Order Stochastic optimization methods for nonconvex finite sums

We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients. The methods fitting into this framework combine line searches and suitably decaying step lengths. A key issue is a two-step sampling at each iteration, which allows us to control the error present in the line-search procedure. Stationarity of limit points is proved in the almost-sure sense, while almost-sure convergence of the sequence of approximations to the solution holds with the additional hypothesis that the functions are strongly convex. Numerical experiments, including comparisons with state-of-the art stochastic optimization methods, show the efficiency of our approach.Comment: 22 pages, 4 figure

Post vaccinal temporary sensorineural hearing loss

In our systematic research we identified four studies concerning the onset of neurological adverse events following vaccination and two excluding this association. A 33-year-old Italian man, belonging to the Italian Army was hospitalized because he suffered from vertigo, nausea and sudden right hearing loss not classified (NDD), that set in 24 h after the administration of tetanus-diphtheria and meningococcal vaccines. Some neurological events arising after vaccination are very difficult to treat. In our case, the functional recovery on low and medium frequencies was possible about 6 months after the morbid event

Successful endovascular embolization of a giant splenic artery pseudoaneurysm secondary to a huge pancreatic pseudocyst with concomitant spleen invasion

Pseudoaneurysms of the pancreatic and peripancreatic arteries is a well-known complication of chronic or necrotizing pancreatitis due to proteolytic enzymatic digestion of the arterial wall. A major part of peripancreatic pseudoaneurysms involve the splenic artery, but any peripancreatic artery may be involved and bleed. They are potentially life threatening for patients, due to spontaneous intraperitoneal rupture, rupture and fistulization into the surrounding organs, or fistulization into the pancreatic duct. Small ones are usually asymptomatic and are often diagnosed incidentally, while giant (> 5 cm) aneurysms and pseudoaneurysms are symptomatic and may be detected as a pulsatile mass in the upper-left quadrant or epigastrium. Imaging plays a key role in the identification of splenic artery aneurysms and pseudoaneurysms, while angiography still represents the gold standard for the diagnosis, although nowadays it plays a prominent role in treatment. Treatment of splenic artery pseudoaneurysms is mandatory because of the high probability of rupture, with a mortality rate of up to 90%. The gold standard treatment is represented by surgery, with a mortality rate between 16% and 50%. In recent years the endovascular approach has proven to be an effective alternative treatment for splenic artery pseudoaneurysms, and it is currently the method of choice. In this article, we present the case of a ant pseudoaneurysm of the splenic artery due to huge pseudocysts in a young alcoholic patient with recurrent and chronic pancreatitis, complicated by fistulization and invasion of spleen parenchyma and arteriovenous fistula

Faecal calprotectin and ultrasonography as non-invasive screening tools for detecting colorectal polyps in children with sporadic rectal bleeding. a prospective study

Background: Colorectal polyps are reported in 6,1% of paediatric colonoscopies and in 12% of those performed for lower gastrointestinal bleeding. Although colonoscopy is widely used in paediatric patients, it requires bowel preparation and general anaesthesia or deep sedation, and in rare cases, it can cause complications. Non-invasive screening techniques able to predict polyps in children with isolated and sporadic rectal bleeding may play a key role in the selection of patients needing colonoscopy. Methods: We enrolled all children undergoing colonoscopy for isolated and sporadic rectal bleeding to determine the diagnostic accuracy of faecal calprotectin, ultrasonography (US) and digital rectal examination as diagnostic methods for screening colorectal polyps. Results: A total of 26 of 59 enrolled patients (44.1%) had colonic polyps, one patient had multiple polyps, and 23% of children had polyps proximal to the splenic flexure. The diagnostic accuracy of faecal calprotectin for detecting colorectal polyps was 96.6%, with a sensitivity of 100%. False-positive faecal calprotectin was shown in 2 patients with non-steroidal anti-inflammatory drug-related lesions. The diagnostic accuracy of ultrasound was 77.9%. Polyps not seen with ultrasound tended to be relatively smaller (1.5 vs 2.3, p = 0.001) and located in the rectum. The combined use of FC, US and digital rectal examination obtained a specificity and PPV of 100%. Conclusions: FC combined with US and digital rectal examination is a good and promising non-invasive screening test for detecting colorectal polyps in children with isolated and sporadic rectal bleeding

Pelvic pain in reproductive age: US findings

Pelvic pain in reproductive age often represents a diagnostic challenge due to the variety of potential causes characterized by overlapping clinical symptoms, including gynecological and other disorders (e.g., entero-colic or urological). It is also necessary to determine if there is a possibility of pregnancy to rule out any related complications, such as ectopic pregnancy. Although ultrasound (US), computed tomography (CT), and magnetic resonance imaging (MRI) are strongly integrated, the choice of which is the ideal diagnostic tool should be guided both by clinical suspicion (gynecological vs. non-gynecological cause) and by the risk ratio-benefit (ionizing radiation and instrumental costs), too. The didactic objective proposed by this review consists in the diagnosis of the cause and differential of pelvic pain in reproductive age by describing and critically analyzing the US diagnostic clues of the most frequent adnexal, uterine, and vascular causes