The Forward-Backward-Forward Method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces

Tseng's forward-backward-forward algorithm is a valuable alternative for Korpelevich's extragradient method when solving variational inequalities over a convex and closed set governed by monotone and Lipschitz continuous operators, as it requires in every step only one projection operation. However, it is well-known that Korpelevich's method converges and can therefore be used also for solving variational inequalities governed by pseudo-monotone and Lipschitz continuous operators. In this paper, we first associate to a pseudo-monotone variational inequality a forward-backward-forward dynamical system and carry out an asymptotic analysis for the generated trajectories. The explicit time discretization of this system results into Tseng's forward-backward-forward algorithm with relaxation parameters, which we prove to converge also when it is applied to pseudo-monotone variational inequalities. In addition, we show that linear convergence is guaranteed under strong pseudo-monotonicity. Numerical experiments are carried out for pseudo-monotone variational inequalities over polyhedral sets and fractional programming problems

The Boosted DC Algorithm for Clustering with Constraints

This paper aims to investigate the effectiveness of the recently proposed Boosted Difference of Convex functions Algorithm (BDCA) when applied to clustering with constraints and set clustering with constraints problems. This is the first paper to apply BDCA to a problem with nonlinear constraints. We present the mathematical basis for the BDCA and Difference of Convex functions Algorithm (DCA), along with a penalty method based on distance functions. We then develop algorithms for solving these problems and computationally implement them, with publicly available implementations. We compare old examples and provide new experiments to test the algorithms. We find that the BDCA method converges in fewer iterations than the corresponding DCA-based method. In addition, BDCA yields faster CPU running-times in all tested problems

Assessing the efficacy and safety of magnesium sulfate for management of autonomic nervous system dysregulation in Vietnamese children with severe hand foot and mouth disease.

BACKGROUND: Brainstem encephalitis is a serious complication of hand foot and mouth disease (HFMD) in children. Autonomic nervous system (ANS) dysregulation and hypertension may occur, sometimes progressing to cardiopulmonary failure and death. Vietnamese national guidelines recommend use of milrinone if ANS dysregulation with Stage 2 hypertension develops. We wished to investigate whether magnesium sulfate (MgSO4) improved outcomes in children with HFMD if used earlier in the evolution of the ANS dysregulation (Stage 1 hypertension). METHODS: During a regional epidemic we conducted a randomized, double-blind, placebo-controlled trial of MgSO4 in children with HFMD, ANS dysregulation and Stage 1 hypertension, at the Hospital for Tropical Diseases in Ho Chi Minh city. Study participants received an infusion of MgSO4 or matched placebo for 72 h. We also reviewed data from non-trial HFMD patients in whom milrinone failed to control hypertension, some of whom received MgSO4 as second line therapy. The primary outcome for both analyses was a composite of disease progression within 72 h - addition of milrinone (trial participants only), need for ventilation, shock, or death. RESULTS: Between June 2014 and September 2016, 14 and 12 participants received MgSO4 or placebo respectively, before the trial was stopped due to futility. Among 45 non-trial cases with poorly controlled hypertension despite high-dose milrinone, 33 received MgSO4 while 12 did not. There were no statistically significant differences in the composite outcome between the MgSO4 and the placebo/control groups in either study (adjusted relative risk (95%CI) of [6/14 (43%) vs. 6/12 (50%)], 0.84 (0.37, 1.92), p = 0.682 in the trial and [1/33 (3%) vs. 2/12 (17%)], 0.16 (0.01, 1.79), p = 0.132 in the observational cohort). The incidence of adverse events was similar between the groups. Potentially toxic magnesium levels occurred very rarely with the infusion regime used. CONCLUSION: Although we could not demonstrate efficacy in these studies, there were no safety signals associated with use of 30-50 mg/kg/hr. MgSO4 in severe HFMD. Intermittent outbreaks of HFMD are likely to continue across the region, and an adequately powered trial is still needed to evaluate use of MgSO4 in controlling hypertension in severe HFMD, potentially involving a higher dose regimen. TRIAL REGISTRATION: ClinicalTrials.gov Identifier: NCT01940250 (Registered 22 AUG 2013). Trial sponsor: University of Oxford

Prospects for Food Fermentation in South-East Asia, Topics From the Tropical Fermentation and Biotechnology Network at the End of the AsiFood Erasmus+Project

Fermentation has been used for centuries to produce food in South-East Asia and some foods of this region are famous in the whole world. However, in the twenty first century, issues like food safety and quality must be addressed in a world changing from local business to globalization. In Western countries, the answer to these questions has been made through hygienisation, generalization of the use of starters, specialization of agriculture and use of long-distance transportation. This may have resulted in a loss in the taste and typicity of the products, in an extensive use of antibiotics and other chemicals and eventually, in a loss in the confidence of consumers to the products. The challenges awaiting fermentation in South-East Asia are thus to improve safety and quality in a sustainable system producing tasty and typical fermented products and valorising by-products. At the end of the “AsiFood Erasmus+ project” (www.asifood.org), the goal of this paper is to present and discuss these challenges as addressed by the Tropical Fermentation Network, a group of researchers from universities, research centers and companies in Asia and Europe. This paper presents current actions and prospects on hygienic, environmental, sensorial and nutritional qualities of traditional fermented food including screening of functional bacteria and starters, food safety strategies, research for new antimicrobial compounds, development of more sustainable fermentations and valorisation of by-products. A specificity of this network is also the multidisciplinary approach dealing with microbiology, food, chemical, sensorial, and genetic analyses, biotechnology, food supply chain, consumers and ethnology

Convergence rate of a gradient projection method for solving variational inequalities

Under the error bound assumption, we establish the linear convergence rate of a gradient projection method for solving co-coercive variational inequalities. Using this result, we unify and improve several results in variational inequalities, fixed point problems, and convex feasible problems. Numerical experiments are conducted to illustrate the theoretical results.</p

A note on the weak convergence of the extragradient method for solving pseudo-monotone variational inequalities

A corrigendum in Vuong (J Optim Theory Appl 176:399–409, 2018) is given

On the weak convergence of the extragradient method for solving pseudo-monotone variational inequalities

In infinite-dimensional Hilbert spaces, we prove that the iterative sequence generated by the extragradient method for solving pseudo-monotone variational inequalities converges weakly to a solution. A class of pseudo-monotone variational inequalities is considered to illustrate the convergent behavior. The result obtained in this note extends some recent results in the literature; especially, it gives a positive answer to a question raised in Khanh (Acta Math Vietnam 41:251–263, 2016)

The global exponential stability of a dynamical system for solving variational inequalities

We revisit a dynamical system for solving variational inequalities. Under strongly pseudomonotone and Lipschitz continuous assumptions of the considered operator, we obtain the global exponential stability of the trajectories. Numerical examples are presented confirming the theoretical results. The stability result obtained in this paper improves and complements some recent works