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The impact of stochastic noisy feedback on distributed network utility maximization

IEEE TRANSACTIONS ON INFORMATION THEORY 2008年第2期54卷 645-665页

作者： Zhang, Junshan Zheng, Dong Chiang, Mung Arizona State Univ Ira A Fulton Sch Engn Dept Elect Engn Tempe AZ 85287 USA NextWave Broadband Inc San Diego CA 92130 USA Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

The implementation of distributed network utility maximization (NUM) algorithms hinges heavily on information feedback through message passing among network elements. In practical systems the feedback is often obtained using error-prone measurement mechanisms and suffers from random errors. In this paper, we investigate the impact of noisy feedback on distributed NUM. We first study the distributed NUM algorithms based on the Lagrangian dual method, and focus on the primal-dual (P-D) algorithm, which is a single time-scale algorithm in the sense that the primal and dual parameters are updated simultaneously. Assuming strong duality, we study both cases when the stochastic gradients are unbiased or biased, and develop a general theory on the stochastic stability of the P-D algorithms in the presence of noisy feedback. When the gradient estimators are unbiased, we establish, via a combination of tools in Martingale theory and convex analysis, that the iterates generated by distributed P-D algorithms converge with probability one to the optimal point, under standard technical conditions. In contrast, when the gradient estimators are biased, we show that the iterates converge to a contraction region around the optimal point, provided that the biased terms are asymptotically bounded by a scaled version of the true gradients. We also investigate the rate of convergence for the unbiased case, and find that, in general, the limit process of the interpolated process corresponding to the normalized iterate sequence is a stationary reflected linear diffusion process, not necessarily a Gaussian diffusion process. We apply the above general theory to investigate stability of cross-layer rate control for joint congestion control and random access. Next, we study the impact of noisy feedback on distributed two time-scale NUM algorithms based on primal decomposition. We establish, via the mean ODE method, the convergence of the stochastic two time-scale algorithm under mild conditi

关键词： multihop wireless networks network utility maximization noisy feedback primal-dual algorithm stochastic approximation stochastic networks two time-scale algorithm

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Variational image fusion approach based on TGV and local information

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IET COMPUTER VISION 2018年第4期12卷 535-541页

作者： Wang, Qinxia Yang, Xiaoping Nanjing Univ Sci & Technol Sch Sci Nanjing 210094 Jiangsu Peoples R China Nanjing Univ Dept Math Nanjing 210093 Jiangsu Peoples R China

In this study, the authors propose a variational approach based on total generalised variation (TGV) and local gradient information to fuse multi-focus images as well as medical images of computed tomography and magnetic resonance. They use the second-order TGV as the regularisation term and local gradient information as the fusion weight to extract image features. To compute the new model effectively, the primal-dual algorithm is carried out. Various experiments are made to verify the effectiveness of the proposed methods.

关键词： image fusion feature extraction gradient methods medical image processing computerised tomography biomedical MRI variational image fusion approach total generalised variation local gradient information computed tomography medical images magnetic resonance second-order TGV image feature extraction primal-dual algorithm

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Real-time dynamic MRI using parallel dictionary learning and dynamic total variation

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NEUROCOMPUTING 2017年 238卷 410-419页

作者： Wang, Yang Cao, Ning Liu, Zuojun Zhang, Yudong Hohai Univ Sch Comp & Informat Nanjing 210098 Jiangsu Peoples R China Taizhou Univ Sch Phys & Elect Engn Taizhou 318000 Zhejiang Peoples R China Nanjing Normal Univ Sch Comp Sci & Technol Nanjing 210023 Jiangsu Peoples R China

One of the technical challenges in dynamic magnetic resonance imaging (dMRI) is to obtain MR images with high spatiotemporal resolution in a short scan time. Current state-of-the-art recovery algorithms exploit both spatial and temporal sparsity in dMRI to improve the reconstruction quality. In this paper, we proposed a novel algorithm based on 4-frame parallel dictionary learning and dynamic total variation (PDLDTV) for real-time dMRI reconstruction. The dMRI sequence was decomposed into 4-frame subsets and each subset included the first frame (obtained with more k-space sampling for reference to later frames) and any adjacent three frames. A 3D patch-based dictionary learning algorithm and a dynamic total variation algorithm were used to exploit the spatiotemporal sparsity in each subset. High algorithm speed was required for our real-time reconstruction, and a primal-dual algorithm was used to solve the challenging problem. Experiments over two cardiac dMRI sequences indicated that the proposed 4-frame PDLDTV showed better reconstruction performance than the state-of-the-art online and offline methods such as DTV, k-t SLR, and DLTG. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Dynamic magnetic resonance imaging Dictionary learning Dynamic total variation primal-dual algorithm

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Asynchronous distributed voltage control in active distribution networks

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AUTOMATICA 2020年 122卷 109269-109269页

作者： Wang, Zhaojian Liu, Feng Su, Yifan Yang, Peng Qin, Boyu Shanghai Jiao Tong Univ Dept Automat Key Lab Syst Control & Informat Proc Minist Educ China Shanghai 200240 Peoples R China Tsinghua Univ Dept Elect Engn State Key Lab Power Syst Beijing 100084 Peoples R China Xi An Jiao Tong Univ Sch Elect Engn State Key Lab Elect Insulat & Power Equipment Xian 710049 Peoples R China

With the proliferation of distributed energy resources (DERs), voltage regulation in active distribution networks (ADNs) has been facing a great challenge. This paper derives an asynchronous distributed voltage control strategy based on the partial primal-dual gradient algorithm, where both active and reactive power of DERs are considered. Different types of asynchrony due to imperfect communication or other practical limits, such as random time delays and non-identical sampling/computation rates, are fitted into a unified analytic framework. The proposed asynchronous algorithm is then converted into a fixed-point problem by leveraging the operator splitting method, which leads to the convergence proof. Moreover, an online implementation method is introduced to make the controller adjustable to time-varying environments. Finally, numerical experiments are carried out on a rudimentary 8-bus and the IEEE-123 bus system to verify the effectiveness of the proposed method. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： Distributed control Active distribution networks primal-dual algorithm Asynchronous algorithm Voltage control

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Minimizing a linear multiplicative-type function under network flow constraints

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OPERATIONS RESEARCH LETTERS 1997年第3期20卷 141-148页

作者： Kuno, T Utsunomiya, T Institute of Information Sciences and Electronics University of Tsukuba Tsukuba Ibaraki 305 Japan

In this paper, we consider a special class of nonconvex network flow problems, whose objective function is a product of two affine functions. This problem arises when one tries to send as much flow as possible in an ordinary two-terminal network at the minimum possible cost. We will show that a primal-dual algorithm can generate a globally optimal solution in pseudo-polynomial time and a globally epsilon-optimal solution in polynomial time. (C) 1997 Elsevier Science B.V.

关键词： global optimization linear multiplicative programming nonconvex cost network flow bicriteria decision making primal-dual algorithm

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A Convex Approach for Image Restoration with Exact Poisson-Gaussian Likelihood

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SIAM JOURNAL ON IMAGING SCIENCES 2015年第4期8卷 2662-2682页

作者： Chouzenoux, Emilie Jezierska, Anna Pesquet, Jean-Christophe Talbot, Hugues Univ Paris Est Marne La Vallee LIGM F-77454 Marne La Vallee France Polish Acad Sci Syst Res Inst Dept Modelling & Optimizat Dynam Syst PL-01447 Warsaw Poland ESIEE LIGM F-93162 Noisy Le Grand France

The Poisson-Gaussian model can accurately describe the noise present in a number of imaging systems. However most existing restoration methods rely on approximations of the Poisson-Gaussian noise statistics. We propose a convex optimization strategy for the reconstruction of images degraded by a linear operator and corrupted with a mixed Poisson-Gaussian noise. The originality of our approach consists of considering the exact, mixed continuous-discrete model corresponding to the data statistics. After establishing the Lipschitz differentiability and convexity of the Poisson-Gaussian neg-log-likelihood, we derive a primal-dual iterative scheme for minimizing the associated penalized criterion. The proposed method is applicable to a large choice of convex penalty terms. The robustness of our scheme allows us to handle computational difficulties due to infinite sums arising from the computation of the gradient of the criterion. We propose finite bounds for these sums, that are dependent on the current image estimate, and thus adapted to each iteration of our algorithm. The proposed approach is validated on image restoration examples. Then, the exact data fidelity term is used as a reference for studying some of its various approximations. We show that in a variational framework the shifted Poisson and exponential approximations lead to very good restoration results.

关键词： Poisson-Gaussian noise convex optimization proximal methods primal-dual algorithm image restoration

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An almost-linear time and linear space algorithm for the longest common subsequence problem

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INFORMATION PROCESSING LETTERS 2005年第3期94卷 131-135页

作者： Guo, JY Hwang, FK Natl Chiao Tung Univ Dept Appl Math Hsinchu 30500 Taiwan

There are two general approaches to the longest common subsequence problem. The dynamic programming approach takes quadratic time but linear space, while the nondynamic-programming approach takes less time but more space. We propose a new implementation of the latter approach which seems to get the best for both time and space for the DNA application. (c) 2005 Elsevier B.V. All rights reserved.

关键词： algorithms primal-dual algorithm longest common subsequence

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BI-LEVEL PROGRAMMING FOR EMERGENCY BLOOD TRANSSHIPMENT-ALLOCATION CONSIDERING SUBSTITUTION AGAINST PUBLIC HEALTH EVENTS

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2024年第8期20卷 2697-2718页

作者： Cheng, Jiahao Zhou, Yufeng Teo, Kok lay Chongqing Technol & Business Univ Sch Management Sci & Engn Chongqing 400067 Peoples R China Chongqing Technol & Business Univ Res Ctr Econ Upper Reaches Yangtze River Chongqing 400067 Peoples R China Sunway Univ Sch Math Sci Bandar Sunway 47500 Selangor Malaysia

. The emergence of major public health crises, such as the Covid-19 pandemic, has significantly impacted the blood supply chain. We developed a bi-level programming model for emergency blood transshipment-allocation under this scenario, based on a cross-regional blood transshipment allocation network with a hierarchical structure. Our model considers emergency allocation, blood acceptability limits, blood type substitution relationships, hierarchical relationships among scheduling networks, and cross-regional and multi-modal transportation. The upper-level objective of our model is to minimize the total system cost, which includes shortage and substitution penalties. The lowerlevel objective is to maximize blood allocation satisfaction while considering demand urgency and blood type substitution. A primal-dual algorithm based on complementary relaxation conditions is established to solve the transformed model. The efficacy of our proposed model and solution strategy is validated through numerical calculations.

关键词： Bi-level programming public health events blood shortage blood substitution primal-dual algorithm

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A stochastic algorithm for online bipartite resource allocation problems

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COMPUTERS & OPERATIONS RESEARCH 2016年 75卷 28-37页

作者： Legrain, Antoine Jaillet, Patrick CIRRELT CP 6079Succursale Ctr Ville Montreal PQ H3C 3A7 Canada Polytech Montreal Dept Math & Ind Engn CP 6079Succursale Ctr Ville Montreal PQ H3C 3A7 Canada MIT Lab Informat & Decis Syst Dept Elect Engn & Comp Sci 77 Massachusetts Ave Cambridge MA 02139 USA MIT Ctr Operat Res Cambridge MA 02139 USA

This paper deals with online resource allocation problems whereby buyers with a limited total budget want to purchase items which become available one at a time and which consume some amount of various limited resources upon allocation. A central resource allocation platform is in charge of allocating the items to the potential buyers, with the goal of maximizing the total revenue subject to budget and resource constraints. Sponsored search advertising is a typical example: in order to maximize revenue, search engines try to choose the best available advertisement to display on a web page resulting from a search query. Two main approaches have been proposed to address such online problems, depending on the assumptions made about the input sequence: one is trying to guarantee a performance against a worst case scenario (sometimes called the adversarial model);the other one, based on specific probabilistic assumptions about the input, is concerned with expected performance guarantee. However, combining the strengths of these two approaches could potentially outperform both in some settings. In this paper we propose such a practical method which goes beyond the adversarial model but requires only a limited amount of information about the future. We provide extensive computational results which demonstrate settings under which the performance of the proposed algorithm becomes attractive. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Resource allocation Online optimization primal-dual algorithm Stochastic optimization L-Shaped method Adwords problem

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Proximal Splitting algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists

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SIAM REVIEW 2023年第2期65卷 375-435页

作者： Condat, Laurent Kitahara, Daichi Contreras, Andres Hirabayashi, Akira King Abdullah Univ Sci & Technol KAUST Visual Comp Ctr Thuwal 239556900 Saudi Arabia Osaka Univ Div Elect Elect & Infocommun Engn Suita Japan UC Temuco Fac Engn Dept Math & Phys Sci Temuco La Araucania Chile Ritsumeikan Univ Coll Informat Sci & Engn Kusatsu 5258577 Japan

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they consist of simple operations, handling the terms in the objective function separately. In this overview, we demystify a selection of recent proximal splitting algorithms: we present them within a unified framework, which consists in applying splitting methods for monotone inclusions in primal-dual product spaces, with well-chosen metrics. Along the way, we easily derive new variants of the algorithms and revisit existing convergence results, extending the parameter ranges in several cases. In particular, we emphasize that when the smooth term in the objective function is quadratic, e.g., for least-squares problems, convergence is guaranteed with larger values of the relaxation parameter than previously known. Such larger values are usually beneficial for the convergence speed in practice.

关键词： large-scale convex optimization nonsmooth optimization splitting proximal algorithm primal-dual algorithm

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