Relevant bibliographies by topics / Alternating direction methods of multipliers

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Academic literature on the topic 'Alternating direction methods of multipliers'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Alternating direction methods of multipliers"

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Suzuki, Taiji. "STOCHASTIC ALTERNATING DIRECTION METHOD OF MULTIPLIERS FOR STRUCTURED REGULARIZATION." Journal of the Japanese Society of Computational Statistics 28, no. 1 (2015): 105–24. http://dx.doi.org/10.5183/jjscs.1502004_218.

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Hager, William W., and Hongchao Zhang. "Inexact alternating direction methods of multipliers for separable convex optimization." Computational Optimization and Applications 73, no. 1 (2019): 201–35. http://dx.doi.org/10.1007/s10589-019-00072-2.

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Ma, Shiqian, Lingzhou Xue, and Hui Zou. "Alternating Direction Methods for Latent Variable Gaussian Graphical Model Selection." Neural Computation 25, no. 8 (2013): 2172–98. http://dx.doi.org/10.1162/neco_a_00379.

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Chandrasekaran, Parrilo, and Willsky ( 2012 ) proposed a convex optimization problem for graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance matrix that can be decomposed into a sparse matrix minus a low-rank matrix from sample data. Solving this convex optimization problem is very challenging, especially for large problems. In this letter, we propose two alternating direction methods for solving this problem. The first method is to apply the classic alternating direction method of multipliers to solve the problem as a consensus problem. The second method is a proximal gradient-based alternating-direction method of multipliers. Our methods take advantage of the special structure of the problem and thus can solve large problems very efficiently. A global convergence result is established for the proposed methods. Numerical results on both synthetic data and gene expression data show that our methods usually solve problems with 1 million variables in 1 to 2 minutes and are usually 5 to 35 times faster than a state-of-the-art Newton-CG proximal point algorithm.
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Yu, Siting, Jingjing Peng, Zengao Tang, and Zhenyun Peng. "Iterative methods to solve the constrained Sylvester equation." AIMS Mathematics 8, no. 9 (2023): 21531–53. http://dx.doi.org/10.3934/math.20231097.

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<abstract><p>In this paper, the multiple constraint least squares solution of the Sylvester equation $ AX+XB = C $ is discussed. The necessary and sufficient conditions for the existence of solutions to the considered matrix equation are given. Noting that the alternating direction method of multipliers (ADMM) is a one-step iterative method, a multi-step alternating direction method of multipliers (MSADMM) to solve the considered matrix equation is proposed and some convergence results of the proposed algorithm are proved. Problems that should be studied in the near future are listed. Numerical comparisons between MSADMM, ADMM and ADMM with Anderson acceleration (ACADMM) are included.</p></abstract>
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Li, Min, Li-Zhi Liao, and Xiaoming Yuan. "Inexact Alternating Direction Methods of Multipliers with Logarithmic–Quadratic Proximal Regularization." Journal of Optimization Theory and Applications 159, no. 2 (2013): 412–36. http://dx.doi.org/10.1007/s10957-013-0334-4.

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Huang, Chunlin, and Dongbo Bu. "Predicting human contacts through alternating direction method of multipliers." International Journal of Modern Physics C 30, no. 07 (2019): 1940014. http://dx.doi.org/10.1142/s012918311940014x.

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Transmission of respiratory infectious diseases depends greatly on human close-proximity contacts, making thorough understanding of current and upcoming contacts essential for epidemic containment. Although different devices and software have been developed for contact data collection, there are few effective methods for contact prediction available in the near future as far as the authors know. In this study, we propose an approach to predict human contacts. We first extract human features together with their significances from the human contacts through alternating direction method of multipliers (ADMM), then predict future significances based on periodicity of contacts, and finally construct future contacts from human features and future significances. With the help of contact data collected in a Chinese University, we compare this approach with a trivial method of directly averaging known contacts. The comparison shows that our approach generates contacts deviating less from the true ones.
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Abeynanda, Hansi K., and G. H. J. Lanel. "A Study on Distributed Optimization over Large-Scale Networked Systems." Journal of Mathematics 2021 (April 29, 2021): 1–19. http://dx.doi.org/10.1155/2021/5540262.

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Distributed optimization is a very important concept with applications in control theory and many related fields, as it is high fault-tolerant and extremely scalable compared with centralized optimization. Centralized solution methods are not suitable for many application domains that consist of large number of networked systems. In general, these large-scale networked systems cooperatively find an optimal solution to a common global objective during the optimization process. Thus, it gives us an opportunity to analyze distributed optimization techniques that is demanded in most distributed optimization settings. This paper presents an analysis that provides an overview of decomposition methods as well as currently existing distributed methods and techniques that are employed in large-scale networked systems. A detailed analysis on gradient like methods, subgradient methods, and methods of multipliers including the alternating direction method of multipliers is presented. These methods are analyzed empirically by using numerical examples. Moreover, an example highlighting the fact that the gradient method fails to solve distributed problems in some circumstances is discussed under numerical results. A numerical implementation is used to demonstrate that the alternating direction method of multipliers can solve this particular problem, by revealing its robustness compared with the gradient method. Finally, we conclude the paper with possible future research directions.
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Chao, Miantao, Caozong Cheng, and Haibin Zhang. "A Linearized Alternating Direction Method of Multipliers with Substitution Procedure." Asia-Pacific Journal of Operational Research 32, no. 03 (2015): 1550011. http://dx.doi.org/10.1142/s0217595915500116.

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We consider the linearly constrained separable convex programming problem whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method of multipliers (ADMM) has been well studied in the literature for the special case m = 2, but the direct extension of ADMM for the general case m ≥ 2 is not necessarily convergent. In this paper, we propose a new linearized ADMM-based contraction type algorithms for the general case m ≥ 2. For the proposed algorithm, we prove its convergence via the analytic framework of contractive type methods and we derive a worst-case O(1/t) convergence rate in ergodic sense. Finally, numerical results are reported to demonstrate the effectiveness of the proposed algorithm.
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Wang, Si, Ting-Zhu Huang, Xi-le Zhao, and Jun Liu. "An Alternating Direction Method for Mixed Gaussian Plus Impulse Noise Removal." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/850360.

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A combined total variation and high-order total variation model is proposed to restore blurred images corrupted by impulse noise or mixed Gaussian plus impulse noise. We attack the proposed scheme with an alternating direction method of multipliers (ADMM). Numerical experiments demonstrate the efficiency of the proposed method and the performance of the proposed method is competitive with the existing state-of-the-art methods.
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Liu, Yang, and Yazheng Dang. "Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem." Journal of Mathematics 2023 (March 28, 2023): 1–12. http://dx.doi.org/10.1155/2023/4316267.

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The alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving various nonconvex consensus problem. The convergence of the conventional ADMM (i.e., 2-block) for convex objective functions has been stated for a long time. As an accelerated technique, the inertial effect was used by many authors to solve 2-block convex optimization problem. This paper combines the ADMM and the inertial effect to construct an inertial alternating direction method of multipliers (IADMM) to solve the multiblock nonconvex consensus problem and shows the convergence under some suitable conditions. Simulation experiment verifies the effectiveness and feasibility of the proposed method.
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Dissertations / Theses on the topic "Alternating direction methods of multipliers"

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Selvatici, Elena. "Variational formulation for Granular Contact Dynamics simulation via the Alternating Direction Method of Multipliers." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021.

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The subject of this thesis is the development of a calculation software for the numerical analysis and the dynamic simulation of a granular flow. One of the major problems encountered in the dynamic analysis of the mechanical behaviour of a granular medium is the enormous computational time taken to reach the solution of the problem. Following studies that have verified the effectiveness of the implicit formulation proposed by the Granular Contact Dynamics approach, the idea of this thesis arises from the desire to apply the Alternating Direction Method of Multipliers for the optimization of the solution, a parallelizable algorithm already validated in similar contexts. The main part of the work consisted in the realization of the program using the Python programming language. During the process particular importance was given to computational optimization, and each part of the program has been designed to handle large scale problems. To generate the starting conditions we have implemented algorithms both for importing and for generating a model, and we have implemented methods for the introduction and management of the static and kinematic boundaries. As for the solution algorithm we reviewed the mathematical model of the GCD: the solution of the problem leads to the application of the principle of minimum of the total potential energy associated with the system. We introduced the augmented Lagrangian: its minimization, with respect to one of the primary variables and assuming the other unknowns as constants, constitutes the core of the ADMM. The software has been included within mechpy, an open source platform for the development of unconventional finite element formulations, and is able to manage both two-dimensional and three-dimensional models. The results are very promising: the output of the simulations has been compared with experimental results, and the noticeable correspondence validates the software functionality.
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Gu, Yan. "STUDIES ON ALTERNATING DIRECTION METHOD OF MULTIPLIERS WITH ADAPTIVE PROXIMAL TERMS FOR CONVEX OPTIMIZATION PROBLEMS." Kyoto University, 2020. http://hdl.handle.net/2433/259758.

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Fécamp, Vivien. "Recalage/Fusion d'images multimodales à l'aide de graphes d'ordres supérieurs." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLC005/document.

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L’objectif principal de cette thèse est l’exploration du recalage d’images à l’aide de champs aléatoires de Markov d’ordres supérieurs, et plus spécifiquement d’intégrer la connaissance de transformations globales comme une transformation rigide, dans la structure du graphe. Notre cadre principal s’applique au recalage 2D-2D ou 3D-3D et utilise une approche hiérarchique d’un modèle de champ de Markov dont le graphe est une grille régulière. Les variables cachées sont les vecteurs de déplacements des points de contrôle de la grille.Tout d’abord nous expliciterons la construction du graphe qui permet de recaler des images en cherchant entre elles une transformation affine, rigide, ou une similarité, tout en ne changeant qu’un potentiel sur l’ensemble du graphe, ce qui assure une flexibilité lors du recalage. Le choix de la métrique est également laissée à l’utilisateur et ne modifie pas le fonctionnement de notre algorithme. Nous utilisons l’algorithme d’optimisation de décomposition duale qui permet de gérer les hyper-arêtes du graphe et qui garantit l’obtention du minimum exact de la fonction pourvu que l’on ait un accord entre les esclaves. Un graphe similaire est utilisé pour réaliser du recalage 2D-3D.Ensuite, nous fusionnons le graphe précédent avec un autre graphe construit pour réaliser le recalage déformable. Le graphe résultant de cette fusion est plus complexe et, afin d’obtenir un résultat en un temps raisonnable, nous utilisons une méthode d’optimisation appelée ADMM (Alternating Direction Method of Multipliers) qui a pour but d’accélérer la convergence de la décomposition duale. Nous pouvons alors résoudre simultanément recalage affine et déformable, ce qui nous débarrasse du biais potentiel issu de l’approche classique qui consiste à recaler affinement puis de manière déformable<br>The main objective of this thesis is the exploration of higher order Markov Random Fields for image registration, specifically to encode the knowledge of global transformations, like rigid transformations, into the graph structure. Our main framework applies to 2D-2D or 3D-3D registration and use a hierarchical grid-based Markov Random Field model where the hidden variables are the displacements vectors of the control points of the grid.We first present the construction of a graph that allows to perform linear registration, which means here that we can perform affine registration, rigid registration, or similarity registration with the same graph while changing only one potential. Our framework is thus modular regarding the sought transformation and the metric used. Inference is performed with Dual Decomposition, which allows to handle the higher order hyperedges and which ensures the global optimum of the function is reached if we have an agreement among the slaves. A similar structure is also used to perform 2D-3D registration.Second, we fuse our former graph with another structure able to perform deformable registration. The resulting graph is more complex and another optimisation algorithm, called Alternating Direction Method of Multipliers is needed to obtain a better solution within reasonable time. It is an improvement of Dual Decomposition which speeds up the convergence. This framework is able to solve simultaneously both linear and deformable registration which allows to remove a potential bias created by the standard approach of consecutive registrations
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Tang, Shuhan. "Spectral Analysis Using Multitaper Whittle Methods with a Lasso Penalty." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1586863604571678.

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Al, Sarray Basad. "Estimation et choix de modèle pour les séries temporelles par optimisation convexe." Besançon, 2016. http://www.theses.fr/2016BESA2084.

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Les séries temporelles sont définies comme une séquence ordonnée d’observation à travers le temps. La structure des séries temporelles est représentée par la somme des composantes indépendantes. Généralement, ces composantes sont estimées indépendamment les unes des autres chaque composant fait partie d’une catégorie particulière. Les modèles Auto régressifs et Moyenne Mobile sont utilisées pour la modélisation des séries chronologiques il y a un grand nombre d’applications telle que le traitement du signal, la finance, l’imagerie médicale le radar, et la communication. […] Cette étude présente quelques-unes des méthodes d’apprentissage machine, et des méthodes convexes pour la sélection de modèle ARMA et l’estimation est basée sur la conversion des modèles ARMA-AR et des modèles ARMA aux modèle espace d’état. […]<br>[…] this study presents some of machine learning and convex methodes for ARMA model selection and estimation based on the conversion between ARMA –AR models and ARMA-State Space Models. Also in this study, for a time series decomposition and time series components analysis some of convex methods are implemented and simulated. The results show the ability of convex methods of analysing and modelling a given series
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Ojha, Abhi. "Coupled Natural Gas and Electric Power Systems." Thesis, Virginia Tech, 2017. http://hdl.handle.net/10919/78666.

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Decreasing gas prices and the pressing need for fast-responding electric power generators are currently transforming natural gas networks. The intermittent operation of gas-fired plants to balance wind generation introduces spatiotemporal fluctuations of increasing gas demand. At the heart of modeling, monitoring, and control of gas networks is a set of nonlinear equations relating nodal gas injections and pressures to flows over pipelines. Given gas demands at all points of the network, the gas flow task aims at finding the rest of the physical quantities. For a tree network, the problem enjoys a closed-form solution; yet solving the equations for practical meshed networks is non-trivial. This problem is posed here as a feasibility problem involving quadratic equalities and inequalities, and is further relaxed to a convex semidefinite program (SDP) minimization. Drawing parallels to the power flow problem, the relaxation is shown to be exact if the cost function is judiciously designed using a representative set of network states. Numerical tests on a Belgian gas network corroborate the superiority of the novel method in recovering the actual gas network state over a Newton-Raphson solver. This thesis also considers the coupled infrastructures of natural gas and electric power systems. The gas and electric networks are coupled through gas-fired generators, which serve as shoulder and peaking plants for the electric power system. The optimal dispatch of coupled natural gas and electric power systems is posed as a relaxed convex minimization problem, which is solved using the feasible point pursuit (FPP) algorithm. For a decentralized solution, the alternating direction method of multipliers (ADMM) is used in collaboration with the FPP. Numerical experiments conducted on a Belgian gas network connected to the IEEE 14 bus benchmark system corroborate significant enhancements on computational efficiency compared with the centralized FPP-based approach.<br>Master of Science
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Velay, Maxime. "Méthodes d’optimisation distribuée pour l’exploitation sécurisée des réseaux électriques interconnectés." Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAT063/document.

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Notre société étant plus dépendante que jamais au vecteur électrique, la moindre perturbation du transport ou de l’acheminement de l’électricité a un impact social et économique important. La fiabilité et la sécurité des réseaux électriques sont donc cruciales pour les gestionnaires de réseaux, en plus des aspects économiques. De plus, les réseaux de transport sont interconnectés pour réduire les coûts des opérations et pour améliorer la sécurité. Un des plus grand défis des gestionnaires des réseaux de transport est ainsi de se coordonner avec les réseaux voisins, ce qui soulève des problèmes liés à la taille du problème, à l’interopérabilité et à la confidentialité des données.Cette thèse se focalise principalement sur la sécurité des opérations sur les réseaux électriques, c’est pourquoi l’évolution des principales caractéristiques des blackouts, qui sont des échecs de la sécurité des réseaux, sont étudiés sur la période 2005-2016. L’approche de cette étude consiste à déterminer quelles sont les principales caractéristiques des incidents de ces 10 dernières années, afin d’identifier ce qui devrait être intégré pour réduire le risque que ces incidents se reproduisent. L’évolution a été étudiée et comparé avec les caractéristiques des blackouts qui se sont produit avant 2005. L’étude se focalise sur les préconditions qui ont mené à ces blackouts et sur les cascades, et particulièrement sur le rôle de la vitesse des cascades. Les caractéristiques importante sont extraites et intégrées dans la suite de notre travail.Un algorithme résolvant un problème préventif d’Optimal Power Flow avec contraintes de sécurité (SCOPF) de manière distribuée est ainsi développé. Ce problème consiste en l’ajout de contraintes qui assure qu’après la perte de n’importe quel appareil d’importance, le nouveau point d’équilibre, atteint suite au réglage primaire en fréquence, respecte les contraintes du système. L’algorithme développé utilise une décomposition fine du problème et est implémenté sous le paradigme multi-agent, basé sur deux catégories d’agents : les appareils et les bus. Les agents sont coordonnés grâce à l’ « Alternating Direction Method of Multipliers (ADMM)» et grâce à un problème de consensus. Cette décomposition procure l’autonomie et la confidentialité nécessaire aux différents acteurs du système, mais aussi, un bon passage à l’échelle par rapport à la taille du problème. Cet algorithme a aussi pour avantage d’être robuste à n’importe quelle perturbation, incluant la séparation du système en plusieurs régions.Puis, pour prendre en compte l’incertitude sur la production créée par les erreurs de prédiction des fermes éoliennes, une approche distribuée à deux étapes est développée pour résoudre un problème d’Optimal Power Flow avec contraintes probabilistes (CCOPF), d’une manière complétement distribuée. Les erreurs de prédiction des fermes éoliennes sont modélisées par des lois normales indépendantes et les écarts par rapport aux plannings de production sont considérés compensés par le réglage primaire en fréquence. La première étape de l’algorithme a pour but de déterminer des paramètres de sensibilités nécessaires pour formuler le problème. Les résultats de cette étape sont ensuite des paramètres d’entrée de la seconde étape qui, elle, résout le problème de CCOPF. Une extension de cette formulation permet d’ajouter de la flexibilité au problème en permettant la réduction de la production éolienne. Cet algorithme est basé sur la même décomposition fine que précédemment où les agents sont également coordonnés par l’ADMM et grâce à un problème de consensus. En conclusion, cet algorithme en deux étapes garantit la confidentialité et l’autonomie des différents acteurs, et est parallèle et adaptée aux plateformes hautes performances<br>Our societies are more dependent on electricity than ever, thus any disturbance in the power transmission and delivery has major economic and social impact. The reliability and security of power systems are then crucial to keep, for power system operators, in addition to minimizing the system operating cost. Moreover, transmission systems are interconnected to decrease the cost of operation and improve the system security. One of the main challenges for transmission system operators is therefore to coordinate with interconnected power systems, which raises scalability, interoperability and privacy issues. Hence, this thesis is concerned with how TSOs can operate their networks in a decentralized way but coordinating their operation with other neighboring TSOs to find a cost-effective scheduling that is globally secure.The main focus of this thesis is the security of power systems, this is why the evolution of the main characteristics of the blackouts that are failures in power system security, of the period 2005-2016 is studied. The approach consists in determining what the major characteristics of the incidents of the past 10 years are, to identify what should be taken into account to mitigate the risk of incidents. The evolution have been studied and compared with the characteristics of the blackouts before 2005. The study focuses on the pre-conditions that led to those blackouts and on the cascades, and especially the role of the cascade speed. Some important features are extracted and later integrated in our work.An algorithm that solve the preventive Security Constrained Optimal Power Flow (SCOPF) problem in a fully distributed manner, is thus developed. The preventive SCOPF problem consists in adding constraints that ensure that, after the loss of any major device of the system, the new steady-state reached, as a result of the primary frequency control, does not violate any constraint. The developed algorithm uses a fine-grained decomposition and is implemented under the multi-agent system paradigm based on two categories of agents: devices and buses. The agents are coordinated with the Alternating Direction method of multipliers in conjunction with a consensus problem. This decomposition provides the autonomy and privacy to the different actors of the system and the fine-grained decomposition allows to take the most of the decomposition and provides a good scalability regarding the size of the problem. This algorithm also have the advantage of being robust to any disturbance of the system, including the separation of the system into regions.Then, to account for the uncertainty of production brought by wind farms forecast error, a two-step distributed approach is developed to solve the Chance-Constrained Optimal Power Flow problem, in a fully distributed manner. The wind farms forecast errors are modeled by independent Gaussian distributions and the mismatches with the initials are assumed to be compensated by the primary frequency response of generators. The first step of this algorithm aims at determining the sensitivity factors of the system, needed to formulate the problem. The results of this first step are inputs of the second step that is the CCOPF. An extension of this formulation provides more flexibility to the problem and consists in including the possibility to curtail the wind farms. This algorithm relies on the same fine-grained decomposition where the agents are again coordinated by the ADMM and a consensus problem. In conclusion, this two-step algorithm ensures the privacy and autonomy of the different system actors and it is de facto parallel and adapted to high performance platforms
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Guiducci, Martina. "Metodo delle Direzioni Alternate per la ricostruzione di immagini Poissoniane." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19501/.

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Il problema della ricostruzione di immagini si propone di eliminare dall'immagine acquisita il blur e ridurre il rumore per ottenerne una che sia simile il più possibile all'oggetto esatto. In termini matematici tale ricostruzione si traduce nella minimizzazione di una funzione obiettivo formata da due termini: la divergenza di Kullback-Leibler, che rappresenta la distanza tra l'immagine acquisita e l'immagine ricostruita, e un termine di regolarizzazione in norma L_1, che esprime delle informazioni aggiuntive sulla soluzione. Tuttavia la divergenza di Kullback-Leibler coinvolge un logaritmo; dunque nei casi in cui l'immagine da ricostruire sia costituita da molti pixel neri, è necessario imporre un vincolo di non negatività sull'argomento del logaritmo e sulla soluzione. Il problema di minimo studiato in questa tesi è quindi un problema di ottimizzazione vincolata, in cui nella funzione obiettivo compare anche un vincolo che obbliga la soluzione a essere non negativa. A tal fine l'algoritmo implementato è l'Alternating Direction Method of Multipliers (ADMM). Il metodo delle direzioni alternate richiede a sua volta l'utilizzo dell'Orthant-Wise Limited Memory Quasi-Newton Method, il quale è un metodo di tipo quasi Newton progettato per la risoluzione di problemi generali di grandi dimensioni, regolarizzati in norma L_1. Per determinare la direzione di ricerca, richiede ad ogni iterazione la risoluzione di un sistema lineare la cui matrice dei coefficienti è la matrice Hessiana. Questa modalità del calcolo della direzione di ricerca non tiene conto della forma dell'Hessiana. Pertanto è stata proposta una modifica al metodo OWLQN che tenesse conto delle caratteristiche peculiari del problema e quindi della forma dell'Hessiana, in modo tale da poter invertire velocemente quest'ultima in uno spazio di Fourier e rendere il metodo più efficiente. Infine, è stata condotta un'analisi sperimentale sull'immagine oggetto di studio, facendo il confronto tra i metodi impiegati.
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Recupero, Giuseppe Antonio. "Un modello variazionale non convesso per il denoising di superfici." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23210/.

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La scannerizzazione 3D di un oggetto produce una mesh triangolata soggetta a rumore. Il processo di denoising ha l’obiettivo di rimuovere il rumore e ricostruire la superficie originale, mantenendone i dettagli come spigoli, angoli o creste. Presentiamo un nuovo modello variazionale non convesso per il denoising di superfici. La funzione costo, dipendente dai vertici, è formata da un termine di fedeltà in norma L2 e da un termine di penalità definito tramite una versione riscalata e riparametrizzata della funzione Minimax Concave Penalty (MCP). Il problema di minimizzazione è risolto usando il metodo ADMM. Ne risulta un processo iterativo, costituito da tre sottoproblemi, di cui due con soluzione esatta e uno con soluzione approssimata. I risultati sperimentali mostrano la convergenza dell’algoritmo e la sua efficacia, a livello sia qualitativo sia quantitativo, nel rimuovere il rumore preservando le caratteristiche geometriche della superficie. Il processo di denoising riesce inoltre a rendere più regolari e uniformi le triangolazioni, riducendo il numero di facce sovrapposte o degeneri.
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Scrivanti, Gabriele Luca Giovanni. "Nonsmooth Nonconvex Variational Reconstruction for Electrical Impedance Tomography." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20700/.

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Abstract:
Electrical Impedance Tomography is an imaging technique that aims to reconstruct the inner conductivity distribution of a medium starting from a set of measured voltages registered by a series of electrodes that are positioned on the surface of the medium. Such technique was used for the first time in geological studies in 1930 and then applied to industrial procedures. The first clinical use of EIT dates back to 1987. In 2018 EIT was validated in tissue engineering as a noninvasive and label-free imaging and monitoring tool for cell distribution (cell growth, differentiation and tissue formation) in 3D scaffolds. EIT problem can be split into a Forward and an Inverse problem. The aim of Forward EIT is to define the set of measured voltages starting from a known conductivity distribution. If the forward problem is characterized by a nonlinear mapping, called Forward Operator, from the conductivity distribution to the measured voltages, inverse EIT consists of inverting the Forward Operator. This leads to an ill-posed problem which requires regularization, either in the model or in the numerical method that is applied to define the solution. The inverse problem is modelled as a Nonlinear Least Squares problem, where one seeks to minimize the mismatch beetween the measured voltages and the ones generated by the reconstructed conductivity. Reconstruction techniques require the introduction of a regularization term which forces the reconstructed data to stick to certain prior information. In this dissertation, some state-of-the-art regularization methods are analyzed and compared via EIDORS, a specific software for EIT problems. The aim is to reconstruct the variation in conductivity within a 2D section of a 3D scaffold. Furthermore a variational formulation on a 2D mesh for a space-variant regularization is proposed, based on a combination of high order and nonconvex operators, which respectively seek to recover piecewise inhomogeneous and piecewise linear regions.
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Books on the topic "Alternating direction methods of multipliers"

1

Lin, Zhouchen, Huan Li, and Cong Fang. Alternating Direction Method of Multipliers for Machine Learning. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9840-8.

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United States. National Aeronautics and Space Administration., ed. Multi-partitioning for ADI-schemes on message passing architectures. MCAT Institute, 1994.

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United States. National Aeronautics and Space Administration., ed. Multi-partitioning for ADI-schemes on message passing architectures. MCAT Institute, 1994.

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United States. National Aeronautics and Space Administration., ed. Multi-partitioning for ADI-schemes on message passing architectures. MCAT Institute, 1994.

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Baysal, Oktay. Efficient gradient-based shape optimization methodology using inviscid/viscous CFD: Summary of research report for the period of March 9, 1995 to March 8, 1997, grant# NCC-1-211. Dept. of Aerospace Engineering, College of Engineering and Technology, Old Dominion University, 1997.

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United States. National Aeronautics and Space Administration., ed. Efficient gradient-based shape optimization methodology using inviscid/viscous CFD: Summary of research report for the period of March 9, 1995 to March 8, 1997, grant# NCC-1-211. Dept. of Aerospace Engineering, College of Engineering and Technology, Old Dominion University, 1997.

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United States. National Aeronautics and Space Administration., ed. Efficient gradient-based shape optimization methodology using inviscid/viscous CFD: Summary of research report for the period of March 9, 1995 to March 8, 1997, grant# NCC-1-211. Dept. of Aerospace Engineering, College of Engineering and Technology, Old Dominion University, 1997.

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D, Salas M., and Langley Research Center, eds. Three-dimensional simulation of vortex breakdown. National Aeronautics and Space Administration, Langley Research Center, 1990.

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D, Salas M., and Langley Research Center, eds. Three-dimensional simulation of vortex breakdown. National Aeronautics and Space Administration, Langley Research Center, 1990.

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Kuruvila, G. Three-dimensional simulation of vortex breakdown. National Aeronautics and Space Administration, Langley Research Center, 1990.

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Book chapters on the topic "Alternating direction methods of multipliers"

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Glowinski, Roland. "On Alternating Direction Methods of Multipliers: A Historical Perspective." In Computational Methods in Applied Sciences. Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-017-9054-3_4.

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Yan, Ming, and Wotao Yin. "Self Equivalence of the Alternating Direction Method of Multipliers." In Splitting Methods in Communication, Imaging, Science, and Engineering. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41589-5_5.

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Lin, Zhouchen, Huan Li, and Cong Fang. "Derivations of ADMM." In Alternating Direction Method of Multipliers for Machine Learning. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9840-8_2.

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Lin, Zhouchen, Huan Li, and Cong Fang. "ADMM for Nonconvex Optimization." In Alternating Direction Method of Multipliers for Machine Learning. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9840-8_4.

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Lin, Zhouchen, Huan Li, and Cong Fang. "ADMM for Distributed Optimization." In Alternating Direction Method of Multipliers for Machine Learning. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9840-8_6.

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Lin, Zhouchen, Huan Li, and Cong Fang. "ADMM for Deterministic and Convex Optimization." In Alternating Direction Method of Multipliers for Machine Learning. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9840-8_3.

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Lin, Zhouchen, Huan Li, and Cong Fang. "Introduction." In Alternating Direction Method of Multipliers for Machine Learning. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9840-8_1.

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Lin, Zhouchen, Huan Li, and Cong Fang. "Practical Issues and Conclusions." In Alternating Direction Method of Multipliers for Machine Learning. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9840-8_7.

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Lin, Zhouchen, Huan Li, and Cong Fang. "Stochastic ADMM." In Alternating Direction Method of Multipliers for Machine Learning. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9840-8_5.

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Khakhutskyy, Valeriy, and Dirk Pflüger. "Alternating Direction Method of Multipliers for Hierarchical Basis Approximators." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04537-5_9.

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Conference papers on the topic "Alternating direction methods of multipliers"

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Kadkhodaie, Mojtaba, Konstantina Christakopoulou, Maziar Sanjabi, and Arindam Banerjee. "Accelerated Alternating Direction Method of Multipliers." In KDD '15: The 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 2015. http://dx.doi.org/10.1145/2783258.2783400.

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Routray, Chinmay, and Soumya Ranjan Sahoo. "Emulation Alternating Direction Method of Multipliers." In 2022 Eighth Indian Control Conference (ICC). IEEE, 2022. http://dx.doi.org/10.1109/icc56513.2022.10093531.

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Zhang, Guoqiang, and Richard Heusdens. "Bi-alternating direction method of multipliers." In ICASSP 2013 - 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2013. http://dx.doi.org/10.1109/icassp.2013.6638272.

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Wei, Ermin, and Asuman Ozdaglar. "Distributed Alternating Direction Method of Multipliers." In 2012 IEEE 51st Annual Conference on Decision and Control (CDC). IEEE, 2012. http://dx.doi.org/10.1109/cdc.2012.6425904.

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Ling, Qing, and Alejandro Ribeiro. "Decentralized linearized alternating direction method of multipliers." In ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2014. http://dx.doi.org/10.1109/icassp.2014.6854644.

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Routray, Chinmay, and Soumya Ranjan Sahoo. "Decentralizing Consensus-Alternating Direction Method of Multipliers." In 2023 European Control Conference (ECC). IEEE, 2023. http://dx.doi.org/10.23919/ecc57647.2023.10178331.

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Mokhtari, Aryan, Wei Shi, Qing Ling, and Alejandro Ribeiro. "Decentralized quadratically approximated alternating direction method of multipliers." In 2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP). IEEE, 2015. http://dx.doi.org/10.1109/globalsip.2015.7418306.

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Makhdoumi, Ali, and Asuman Ozdaglar. "Broadcast-based distributed alternating direction method of multipliers." In 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2014. http://dx.doi.org/10.1109/allerton.2014.7028466.

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Zhang, Guoqiang, and Richard Heusdens. "Bi-alternating direction method of multipliers over graphs." In ICASSP 2015 - 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2015. http://dx.doi.org/10.1109/icassp.2015.7178636.

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Cerone, V., S. M. Fosson, S. Pirrera, and D. Regruto. "Alternating direction method of multipliers for polynomial optimization." In 2023 European Control Conference (ECC). IEEE, 2023. http://dx.doi.org/10.23919/ecc57647.2023.10178190.

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Reports on the topic "Alternating direction methods of multipliers"

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Ouyang, Yuyuan, Yumei Chen, Guanghui Lan, Jr Pasiliao, and Eduardo. An Accelerated Linearized Alternating Direction Method of Multipliers. Defense Technical Information Center, 2014. http://dx.doi.org/10.21236/ada595588.

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Yan, Ming, and Wotao Yin. Self Equivalence of the Alternating Direction Method of Multipliers. Defense Technical Information Center, 2014. http://dx.doi.org/10.21236/ada610274.

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Deng, Wei, and Wotao Yin. On the Global and Linear Convergence of the Generalized Alternating Direction Method of Multipliers. Defense Technical Information Center, 2012. http://dx.doi.org/10.21236/ada567407.

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Johnsson, S. L., Youcef Saad, and Martin H. Schultz. Alternating Direction Methods on Multiprocessors. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada161973.

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Lambert, Michael Allen. Field simulation of axisymmetric plasma screw pinches by alternating-direction-implicit methods. Office of Scientific and Technical Information (OSTI), 1996. http://dx.doi.org/10.2172/410408.

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