A View of Lagrangian Relaxation and Its Applications

Gaudioso, Manlio

doi:10.1007/978-3-030-34910-3_17

Cited by 11 publications

(2 citation statements)

References 48 publications

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“…Typically, a standardized and flexible machine learning approach is employed for addressing classification problems. Support vectors delineate the margins of hyperplanes, and their identification involves an optimization process incorporating a regulated objective function by a constraint and error term, utilizing Lagrangian relaxation [ 37 ]. The intricacy of the SVM classification task is contingent on the count of SV rather than the input space dimensionality.…”

Section: Methodsmentioning

confidence: 99%

Prediction of heart failure patients with distinct left ventricular ejection fraction levels using circadian ECG features and machine learning

Al Younis,

Hadjileontiadis,

Khandoker

et al. 2024

PLoS ONE

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Heart failure (HF) encompasses a diverse clinical spectrum, including instances of transient HF or HF with recovered ejection fraction, alongside persistent cases. This dynamic condition exhibits a growing prevalence and entails substantial healthcare expenditures, with anticipated escalation in the future. It is essential to classify HF patients into three groups based on their ejection fraction: reduced (HFrEF), mid-range (HFmEF), and preserved (HFpEF), such as for diagnosis, risk assessment, treatment choice, and the ongoing monitoring of heart failure. Nevertheless, obtaining a definitive prediction poses challenges, requiring the reliance on echocardiography. On the contrary, an electrocardiogram (ECG) provides a straightforward, quick, continuous assessment of the patient’s cardiac rhythm, serving as a cost-effective adjunct to echocardiography. In this research, we evaluate several machine learning (ML)-based classification models, such as K-nearest neighbors (KNN), neural networks (NN), support vector machines (SVM), and decision trees (TREE), to classify left ventricular ejection fraction (LVEF) for three categories of HF patients at hourly intervals, using 24-hour ECG recordings. Information from heterogeneous group of 303 heart failure patients, encompassing HFpEF, HFmEF, or HFrEF classes, was acquired from a multicenter dataset involving both American and Greek populations. Features extracted from ECG data were employed to train the aforementioned ML classification models, with the training occurring in one-hour intervals. To optimize the classification of LVEF levels in coronary artery disease (CAD) patients, a nested cross-validation approach was employed for hyperparameter tuning. HF patients were best classified using TREE and KNN models, with an overall accuracy of 91.2% and 90.9%, and average area under the curve of the receiver operating characteristics (AUROC) of 0.98, and 0.99, respectively. Furthermore, according to the experimental findings, the time periods of midnight-1 am, 8–9 am, and 10–11 pm were the ones that contributed to the highest classification accuracy. The results pave the way for creating an automated screening system tailored for patients with CAD, utilizing optimal measurement timings aligned with their circadian cycles.

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Section: Methodsmentioning

confidence: 99%

Prediction of heart failure patients with distinct left ventricular ejection fraction levels using circadian ECG features and machine learning

Al Younis,

Hadjileontiadis,

Khandoker

et al. 2024

PLoS ONE

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“…To provide lower bounds for the BLMST problem, we employed a methodology inspired by the Lagrangian Relaxation method, previously adopted in other MST problem extensions [27,31], as well as in other contexts including assignment, network optimization, and wireless sensor network problems [32]. This involves the creation of a Lagrangian relaxation for the problem and the resolution of its associated Lagrangian dual.…”

Section: Lagrangian Approachmentioning

confidence: 99%

The Budgeted Labeled Minimum Spanning Tree Problem

Cerulli,

D'Ambrosio,

Serra

et al. 2024

Mathematics

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In order to reduce complexity when designing multi-media communication networks, researchers often consider spanning tree problems defined on edge-labeled graphs. The earliest setting addressed in the literature aims to minimize the number of different media types, i.e., distinct labels, used in the network. Despite being extensively addressed, such a setting completely ignores edge costs. This led to the definition of more realistic versions, where budgets for the total cost, or the number of distinct labels allowed, were introduced. In this paper, we introduce and prove the NP-hardness of the Budgeted Labeled Minimum Spanning Tree problem, consisting in minimizing the cost of a spanning tree while satisfying specified budget constraints for each label type. This problem combines the challenges of cost efficiency and label diversity within a fixed budgetary framework, providing a more realistic and practical approach to network design. We provide three distinct mathematical programming formulations of the problem and design a Lagrangian approach to derive tighter lower bounds for the optimal solution of the problem. The performances of the proposed methods are assessed by conducting a series of computational experiments on a variety of randomly generated instances, which showed how the complexity of the problem increases as the size of the network, as well as the number of labels, increase and the budget restrictions are tightened.

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