Constraint-Coupled Distributed Optimization: A Relaxation and Duality Approach

In this paper, we consider a general challenging distributed optimization setup arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local variable, subject to local and coupling constraints, with the latter involving all the decision variables. We propose a novel fully distributed algorithm based on a relaxation of the primal problem and an elegant exploration of duality theory. Despite its complex derivation, based on several duality steps, the distributed algorithm has a very simple and intuitive structure. That is, each node finds a primal-dual optimal solution pair of a local relaxed version of the original problem and then updates suitable auxiliary local variables. We prove that agents asymptotically compute their portion of an optimal (feasible) solution of the original problem. This primal recovery property is obtained without any averaging mechanism typically used in dual decomposition methods. To corroborate the theoretical results, we show how the methodology applies to an instance of a distributed model-predictive control scheme in a microgrid control scenario

Distributed Primal Decomposition for Large-Scale MILPs

This paper deals with a distributed Mixed-Integer Linear Programming (MILP) set-up arising in several control applications. Agents of a network aim to minimize the sum of local linear cost functions subject to both individual constraints and a linear coupling constraint involving all the decision variables. A key, challenging feature of the considered set-up is that some components of the decision variables must assume integer values. The addressed MILPs are NP-hard, nonconvex and large-scale. Moreover, several additional challenges arise in a distributed framework due to the coupling constraint, so that feasible solutions with guaranteed suboptimality bounds are of interest. We propose a fully distributed algorithm based on a primal decomposition approach and an appropriate tightening of the coupling constraint. The algorithm is guaranteed to provide feasible solutions in finite time. Moreover, asymptotic and finite-time suboptimality bounds are established for the computed solution. Montecarlo simulations highlight the extremely low suboptimality bounds achieved by the algorithm

Distributed Personalized Gradient Tracking with Convex Parametric Models

We present a distributed optimization algorithm for solving online personalized optimization problems over a network of computing and communicating nodes, each of which linked to a specific user. The local objective functions are assumed to have a composite structure and to consist of a known time-varying (engineering) part and an unknown (user-specific) part. Regarding the unknown part, it is assumed to have a known parametric (e.g., quadratic) structure a priori, whose parameters are to be learned along with the evolution of the algorithm. The algorithm is composed of two intertwined components: (i) a dynamic gradient tracking scheme for finding local solution estimates and (ii) a recursive least squares scheme for estimating the unknown parameters via user's noisy feedback on the local solution estimates. The algorithm is shown to exhibit a bounded regret under suitable assumptions. Finally, a numerical example corroborates the theoretical analysis

Enhanced gradient tracking algorithms for distributed quadratic optimization via sparse gain design

In this paper we propose a new control-oriented design technique to enhance the algorithmic performance of the distributed gradient tracking algorithm. We focus on a scenario in which agents in a network aim to cooperatively minimize the sum of convex, quadratic cost functions depending on a common decision variable. By leveraging a recent system-theoretical reinterpretation of the considered algorithmic framework as a closed-loop linear dynamical system, the proposed approach generalizes the diagonal gain structure associated to the existing gradient tracking algorithms. Specifically, we look for closed-loop gain matrices that satisfy the sparsity constraints imposed by the network topology, without however being necessarily diagonal, as in existing gradient tracking schemes. We propose a novel procedure to compute stabilizing sparse gain matrices by solving a set of nonlinear matrix inequalities, based on the solution of a sequence of approximate linear versions of such inequalities. Numerical simulations are presented showing the enhanced performance of the proposed design compared to existing gradient tracking algorithms

The Relativistic Hopfield network: rigorous results

The relativistic Hopfield model constitutes a generalization of the standard Hopfield model that is derived by the formal analogy between the statistical-mechanic framework embedding neural networks and the Lagrangian mechanics describing a fictitious single-particle motion in the space of the tuneable parameters of the network itself. In this analogy the cost-function of the Hopfield model plays as the standard kinetic-energy term and its related Mattis overlap (naturally bounded by one) plays as the velocity. The Hamiltonian of the relativisitc model, once Taylor-expanded, results in a P-spin series with alternate signs: the attractive contributions enhance the information-storage capabilities of the network, while the repulsive contributions allow for an easier unlearning of spurious states, conferring overall more robustness to the system as a whole. Here we do not deepen the information processing skills of this generalized Hopfield network, rather we focus on its statistical mechanical foundation. In particular, relying on Guerra's interpolation techniques, we prove the existence of the infinite volume limit for the model free-energy and we give its explicit expression in terms of the Mattis overlaps. By extremizing the free energy over the latter we get the generalized self-consistent equations for these overlaps, as well as a picture of criticality that is further corroborated by a fluctuation analysis. These findings are in full agreement with the available previous results.Comment: 11 pages, 1 figur

Flavonoid and non-flavonoid compounds of autumn royal and egnatia grape skin extracts affect membrane PUFA's profile and cell morphology in human colon cancer cell lines

Grapes contain many flavonoid and non-flavonoid compounds with anticancer effects. In this work we fully characterized the polyphenolic profile of two grape skin extracts (GSEs), Autumn Royal and Egnatia, and assessed their effects on Polyunsaturated Fatty Acid (PUFA) membrane levels of Caco2 and SW480 human colon cancer cell lines. Gene expression of 15-lipoxygenase-1 (15-LOX-1), and peroxisome proliferator-activated receptor gamma (PPAR-γ), as well as cell morphology, were evaluated. The polyphenolic composition was analyzed by Ultra-High-Performance Liquid Chromatography/Quadrupole-Time of Flight mass spectrometry (UHPLC/QTOF) analysis. PUFA levels were evaluated by gas chromatography, and gene expression levels of 15-LOX-1 and PPAR-γ were analyzed by real-time Polymerase Chain Reaction (PCR). Morphological cell changes caused by GSEs were identified by field emission scanning electron microscope (FE-SEM) and photomicrograph examination. We detected a different profile of flavonoid and non-flavonoid compounds in Autumn Royal and Egnatia GSEs. Cultured cells showed an increase of total PUFA levels mainly after treatment with Autumn Royal grape, and were richer in flavonoids when compared with the Egnatia variety. Both GSEs were able to affect 15-LOX-1 and PPAR-γ gene expression and cell morphology. Our results highlighted a new antitumor mechanism of GSEs that involves membrane PUFAs and their downstream pathways

Factors Influencing Generation Z Bachelor of Nursing Students’ Decision to Choose Nursing as a Career: A Pilot Study

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Psychometric Properties of the Italian Version of the Leader Member Exchange Scale (LMX-7): A Validation Study

For decades, scholars have studied leader–member exchange (LMX) relationships to understand and explain the effects of leadership on follower attitudes and performance outcomes within work settings. One available instrument to measure these aspects is the LMX-7 scale. This measurement has been widely used in empirical studies, but its psychometric properties have been poorly explored. The aim of this study was to test the psychometric characteristics (content, structural and construct validity, and reliability) of the Italian version of the LMX-7 scale and to support its cultural adaptation. We used a cross-sectional multi-center design. The forward–backward translation process was used to develop the Italian version of the scale. The scale was administered through an online survey to 837 nurses and nurse managers working in different settings. The factorial structure was tested using both exploratory and confirmatory factor analyses (EFA and CFA), and reliability was evaluated using Cronbach’s alpha. For the construct validity, we used hypothesis testing and differentiation by known groups. The Italian version of the LMX-7 scale presented one dimension. All the psychometric tests performed confirmed its validity and suggested its usefulness for future research

Predictors of mortality following emergency open colectomy for ischemic colitis: A single-center experience

Background: Ischemic colitis (IC) is a severe emergency in gastrointestinal surgery. The aim of the present study was to identify the predictors of postoperative mortality after emergent open colectomy for IC treatment. Additionally, we compared postoperative outcomes of patients undergoing emergent colectomy due to aortic surgery-related IC (AS-IC group) vs. other IC etiologies (Other-IC group). Methods: We analyzed records of consecutive patients who underwent emergency open colectomy for IC between 2008 and 2019. Logistic regression analysis was performed to identify clinical and operative parameters associated with postoperative mortality. The AS-IC and Other-IC groups were compared for mortality, morbidity, ICU stay, hospital stay, and survival. Results: During the study period, 94 patients (mean age, 67.4 ± 13.7 years) underwent emergent open colectomy for IC. In the majority of cases, IC involved the entire colon (53.2%) and vasopressor agents were required preoperatively (63.8%) and/or intraoperatively (78.8%). Thirty-four patients underwent surgery due to AS-IC, whereas 60 due to Other-IC causes. In the AS-IC group, 9 patients had undergone endovascular aortic repair and 25 open aortic surgery; 61.8% of patients needed aortic surgery for ruptured abdominal aortic aneurism (AAA). Overall, 66 patients (70.2%) died within 90 days from surgery. The AS-IC and Other-IC groups showed similar operative outcomes and postoperative complication rates. However, the duration of the ICU stay (19 days vs. 11 days; p = 0.003) and of the total hospital stay (22 days vs. 16 days; p = 0.016) was significantly longer for the AS-IC group than for the Other-IC group. The rate of intestinal continuity restoration at 1 year after surgery was higher for the Other-IC group than for the AS-IC group (58.8% vs. 22.2%; p = 0.05). In the multivariate model, preoperative increased lactate levels, a delay between signs/symptoms' onset and surgery > 12 h, and the occurrence of postoperative acute kidney injury were statistically associated with postoperative mortality. Neither IC etiology (aortic surgery vs. other etiology) nor ruptured AAA was associated with postoperative mortality. Conclusion: Emergency open colectomy for IC is associated with high postoperative mortality, which appears to be unrelated to the IC etiology. Preoperative lactate levels, > 12-h delay to surgery, and postoperative acute kidney injury are independent predictors of postoperative mortality