A filter algorithm : comparison with NLP solvers

Versão não definitiva do artigoThe purpose of this work is to present an algorithm to solve nonlinear constrained optimization problems, using the filter method with the inexact restoration (IR) approach. In the IR approach two independent phases are performed in each iteration—the feasibility and the optimality phases. The first one directs the iterative process into the feasible region, i.e. finds one point with less constraints violation. The optimality phase starts from this point and its goal is to optimize the objective function into the satisfied constraints space. To evaluate the solution approximations in each iteration a scheme based on the filter method is used in both phases of the algorithm. This method replaces the merit functions that are based on penalty schemes, avoiding the related difficulties such as the penalty parameter estimation and the non-differentiability of some of them. The filter method is implemented in the context of the line search globalization technique. A set of more than two hundred AMPL test problems is solved. The algorithm developed is compared with LOQO and NPSOL software packages.Fundação para a Ciência e a Tecnologia (FCT

Targetable ERBB2 mutation status is an independent marker of adverse prognosis in estrogen receptor positive, ERBB2 non-amplified primary lobular breast carcinoma: a retrospective in silico analysis of public datasets

© 2020 The Author(s). Background: Invasive lobular carcinoma (ILC) accounts for 10-15% of primary breast cancers and is typically estrogen receptor alpha positive (ER+) and ERBB2 non-amplified. Somatic mutations in ERBB2/3 are emerging as a tractable mechanism underlying enhanced human epidermal growth factor 2 (HER2) activity. We tested the hypothesis that therapeutically targetable ERBB2/3 mutations in primary ILC of the breast associate with poor survival outcome in large public datasets. Methods: We performed in silico comparison of ERBB2 non-amplified cases of ER+ stage I-III primary ILC (N = 279) and invasive ductal carcinoma (IDC, N = 1301) using METABRIC, TCGA, and MSK-IMPACT information. Activating mutations amenable to HER2-directed therapy with neratinib were identified using existing functional data from in vitro cell line and xenograft experiments. Multivariate analysis of 10-year overall survival (OS) with tumor size, grade, and lymph node status was performed using a Cox regression model. Differential gene expression analyses by ERBB2 mutation and amplification status was performed using weighted average differences and an in silico model of response to neratinib derived from breast cancer cell lines. Results: ILC tumors comprised 17.7% of all cases in the dataset but accounted for 47.1% of ERBB2-mutated cases. Mutations in ERBB2 were enriched in ILC vs. IDC cases (5.7%, N = 16 vs. 1.4%, N = 18, p < 0.0001) and clustered in the tyrosine kinase domain of HER2. ERBB3 mutations were not enriched in ILC (1.1%, N = 3 vs. 1.8%, N = 23; p = 0.604). Median OS for patients with ERBB2-mutant ILC tumors was 66 months vs. 211 months for ERBB2 wild-type (p = 0.0001), and 159 vs. 166 months (p = 0.733) for IDC tumors. Targetable ERBB2 mutational status was an independent prognostic marker of 10-year OS - but only in ILC (hazard ratio, HR = 3.7, 95% CI 1.2-11.0; p = 0.021). Findings were validated using a novel ERBB2 mutation gene enrichment score (HR for 10-year OS in ILC = 2.3, 95% CI 1.04-5.05; p = 0.040). Conclusions: Targetable ERBB2 mutations are enriched in primary ILC and their detection represents an actionable strategy with the potential to improve patient outcomes. Biomarker-led clinical trials of adjuvant HER-targeted therapy are warranted for patients with ERBB2-mutated primary ILC