On limited-memory quasi-Newton methods for minimizing a quadratic function

The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give two classes of limited-memory quasi-Newton Hessian approximations that generate search directions parallel to those of the method of preconditioned conjugate gradients, and hence give finite termination on quadratic optimization problems. The Hessian approximations are described by a novel compact representation which provides a dynamical framework. We also discuss possible extensions of these classes and show their behavior on randomly generated quadratic optimization problems. The methods behave numerically similar to L-BFGS. Inclusion of information from the first iteration in the limited-memory Hessian approximation and L-BFGS significantly reduces the effects of round-off errors on the considered problems. In addition, we give our compact representation of the Hessian approximations in the full Broyden class for the general unconstrained optimization problem. This representation consists of explicit matrices and gradients only as vector components

Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization

The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems directly, which give high quality solutions, and solving many approximate Newton systems which are computationally less expensive but give lower quality solutions. We propose partial and full approximate solutions to the Newton systems. The specific approximate solution depends on estimates of the active and inactive constraints at the solution. These sets are at each iteration estimated by basic heuristics. The partial approximate solutions are computationally inexpensive, whereas a system of linear equations needs to be solved for the full approximate solution. The size of the system is determined by the estimate of the inactive constraints at the solution. In addition, we motivate and suggest two Newton-like approaches which are based on an intermediate step that consists of the partial approximate solutions. The theoretical setting is introduced and asymptotic error bounds are given. We also give numerical results to investigate the performance of the approximate solutions within and beyond the theoretical framework

A structured modified Newton approach for solving systems of nonlinear equations arising in interior-point methods for quadratic programming

The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high quality solutions, but we are interested in modified Newton systems that are computationally less expensive at the expense of lower quality solutions. We propose a structured modified Newton approach where each modified Jacobian is composed of a previous Jacobian, plus one low-rank update matrix per succeeding iteration. Each update matrix is, for a given rank, chosen such that the distance to the Jacobian at the current iterate is minimized, in both 2-norm and Frobenius norm. The approach is structured in the sense that it preserves the nonzero pattern of the Jacobian. The choice of update matrix is supported by results in an ideal theoretical setting. We also produce numerical results with a basic interior-point implementation to investigate the practical performance within and beyond the theoretical framework. In order to improve performance beyond the theoretical framework, we also motivate and construct two heuristics to be added to the method

Functional, Non-Clonal IgMa-Restricted B Cell Receptor Interactions with the HIV-1 Envelope gp41 Membrane Proximal External Region

The membrane proximal external region (MPER) of HIV-1 gp41 has several features that make it an attractive antibody-based vaccine target, but eliciting an effective gp41 MPER-specific protective antibody response remains elusive. One fundamental issue is whether the failure to make gp41 MPER-specific broadly neutralizing antibodies like 2F5 and 4E10 is due to structural constraints with the gp41 MPER, or alternatively, if gp41 MPER epitope-specific B cells are lost to immunological tolerance. An equally important question is how B cells interact with, and respond to, the gp41 MPER epitope, including whether they engage this epitope in a non-canonical manner i.e., by non-paratopic recognition via B cell receptors (BCR). To begin understanding how B cells engage the gp41 MPER, we characterized B cell-gp41 MPER interactions in BALB/c and C57BL/6 mice. Surprisingly, we found that a significant (∼7%) fraction of splenic B cells from BALB/c, but not C57BL/6 mice, bound the gp41 MPER via their BCRs. This strain-specific binding was concentrated in IgMhi subsets, including marginal zone and peritoneal B1 B cells, and correlated with enriched fractions (∼15%) of gp41 MPER-specific IgM secreted by in vitro-activated splenic B cells. Analysis of Igha (BALB/c) and Ighb (C57BL/6) congenic mice demonstrated that gp41 MPER binding was controlled by determinants of the Igha locus. Mapping of MPER gp41 interactions with IgMa identified MPER residues distinct from those to which mAb 2F5 binds and demonstrated the requirement of Fc CH regions. Importantly, gp41 MPER ligation produced detectable BCR-proximal signaling events, suggesting that interactions between gp41 MPER and IgMa determinants may elicit partial B cell activation. These data suggest that low avidity, non-paratopic interactions between the gp41 MPER and membrane Ig on naïve B cells may interfere with or divert bnAb responses

Peri- and postoperative outcomes in patients with endometriosis undergoing hysterectomy

OBJECTIVES: To assess whether hysterectomy in patients with endometriosis is associated with higher proportion of complications compared with patients without, and whether route of hysterectomy affects this outcome. STUDY DESIGN: This is a population-based retrospective cohort study. Data were prospectively obtained from three National Swedish Registers. Patients undergoing a benign hysterectomy between 2015 and 2017 in Sweden were included in the study and were grouped according to a histology-proven diagnosis of endometriosis. Different hysterectomy modes were compared in patients with endometriosis. Perioperative data and postoperative complications up to 1 year after surgery were collected and measured. RESULTS: In all, 8,747 patients underwent a benign hysterectomy, and 1,166 patients with endometriosis was compared with 7,581 patients without. Patients with endometriosis had higher proportion of complications (adjusted Odds ratio aOR 1.2, 95% CI 1.0-1.4), were more often converted to abdominal hysterectomy (aOR 1.7, 95% CI 1.1-2.6), had higher estimated blood loss (EBL) (200-500 ml; aOR 1.8, 95% CI 1.4-2.3, \u3e500 ml; aOR 3.1, 95% CI 2.2-4.4) and a longer operative time (1-2 h; aOR 2.1, 95% CI 1.4-3.2, \u3e2 h; aOR 4.3, 95% CI 2.7-6.6) than endometriosis-free patients. The conversion rate was 13.8 times higher in total laparoscopic hysterectomy (TLH) compared with robotic-assisted laparoscopic hysterectomy (RATLH) (aOR 13.8, 95% CI 3.6-52.4). CONCLUSION: Higher conversion rate, higher EBL and higher frequency of complications were seen in patients with endometriosis. RATLH was associated with lower conversion rate compared to TLH

Urinary incontinence after surgery for pelvic organ prolapse

Contains fulltext : 117923.pdf (publisher's version ) (Closed access)AIMS: This study focused on the changes in urinary incontinence (UI) rates pre- and postoperatively and identified risk factors which predict the presence of symptoms of urgency urinary incontinence (UUI) or stress urinary incontinence (SUI) after surgery for pelvic organ prolapse (POP) without concomitant or previous anti-incontinence surgery. METHODS: All consecutive women who underwent POP surgery without concomitant or previous anti-incontinence surgery in the years 2004-2010 were included. Assessments were performed preoperatively and at 1-year follow-up, including pelvic organ prolapse quantification score and a standardized urogynecological questionnaire (Urogenital Distress Inventory, UDI). Primary outcome of this study was stress and/or urgency UI postoperatively. Furthermore, this study measured the improvement or worsening of UI following surgery using the UDI. Univariable- and multivariable logistic regression with forward selection procedure was used to identify the risk factors. RESULTS: Nine hundred seven patients were included. De novo SUI appeared in 22% and de novo UUI occurred in 21% of the women. At 1-year 42% were cured for UUI and 39% were recovered from SUI by POP surgery alone. The best predictor for the occurrence of postoperative SUI or UUI was the presence of preoperative SUI or UUI. BMI and chronic obstructive pulmonary disease (COPD) were identified as independent risk factors for postoperative SUI. A recurrence in the anterior compartment protected against SUI postoperatively. CONCLUSIONS: Preoperative SUI or UUI is the most important predictor of SUI and UUI postoperatively. BMI and COPD were identified as important risk factors for SUI. Neurourol. Urodynam. 32: 455-459, 2013. (c) 2012 Wiley Periodicals, Inc