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Randomized optimal consensus of multiagent systems based on a novel intermittent projected subgradient algorithm

OPTIMAL CONTROL APPLICATIONS & METHODS 2020年第5期41卷 1783-1795页

作者： Shi, Zhengqing Zhou, Chuan Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Peoples R China

In this article, a novel intermittent projected subgradient algorithm is presented to solve the randomized optimal consensus problem for heterogeneous multiagent systems with time-varying communication topologies. The multiagent systems achieve the consensus meanwhile minimizing the global objective function n-ary sumation i=1mfi(x)via the proposed algorithm, wheref(i)(x)is the convex objective function of agentiitself. Due to the common Bernoulli distribution adopted in the existing random optimization algorithm without considering the different computing capability of each agent. An individual projection probability is assigned for each agent based on computing capabilities so that either making projection or taking average is chosen according to the above probability which can effectively avoid overload for some agents with lower computing capabilities and improve the reliability of the overall systems. A new sufficient step-size condition is given to ensure all agents converge to the optimal solution with probability one. Finally, a numerical example is also given to validate the proposed method.

关键词： distributed optimization multiagent system random optimization subgradient algorithm

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Control subgradient algorithm for image l₁ regularization

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SIGNAL IMAGE AND VIDEO PROCESSING 2015年第1-Sup期9卷 275-283页

作者： El Mouatasim, Abdelkrim Wakrim, Mohammed Univ Ibn Zohr Fac Polydisplinaire Ouarzazate 45800 Morocco Univ Ibn Zohr Fac Sci Dept Math Agadir Morocco

We consider the class of subgradient methods for solving minimization of a nonsmooth convex function regularized by the discretized l(1) norm models arising in image processing. This class of methods is attractive due to its simplicity;however, they are also known to converge quite slowly. In this paper, we present a control subgradient algorithm (CSA) which preserves the computational simplicity of subgradient methods, but with a convergence rate which is proven to be significantly better, both theoretically and practically. Initial promising numerical results for wavelet-based image deblurring demonstrate the capabilities of CSA.

关键词： subgradient algorithm Nesterov algorithm Step-size control l(1) Regularization Image deblurring

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A Piecewise Monotone subgradient algorithm for Accurate L¹-TV Based Registration of Physical Slices With Discontinuities in Microscopy

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IEEE TRANSACTIONS ON MEDICAL IMAGING 2013年第5期32卷 901-918页

作者： Michalek, Jan Capek, Martin Acad Sci Czech Republic Dept Biomath Inst Physiol CZ-14220 Prague 4 Czech Republic

Image registration tasks are often formulated in terms of minimization of a functional consisting of a data fidelity term penalizing the mismatch between the reference and the target image, and a term enforcing smoothness of shift between neighboring pairs of pixels (a min-sum problem). Most methods for deformable image registration use some form of interpolation between matching control points. The interpolation makes it impossible to account for isolated discontinuities in the deformation field that may appear, e.g., when a physical slice of a microscopy specimen is ruptured by the cutting tool. For registration of neighboring physical slices of microscopy specimens with discontinuities, Janacek proposed an L-1-distance data fidelity term and a total variation (TV) smoothness term, and used a graph-cut (GC) based iterative steepest descent algorithm for minimization. The L-1-TV functional is nonconvex;hence a steepest descent algorithm is not guaranteed to converge to the global minimum. Schlesinger presented transformation of max-sum problems to minimization of a dual quantity called problem power, which is-contrary to the original max-sum functional-convex. Based on Schlesinger's solution to max-sum problems we developed an algorithm for L-1-TV minimization by iterative multi-label steepest descent minimization of the convex dual problem. For Schlesinger's subgradient algorithm we proposed a novel step control heuristics that considerably enhances both speed and accuracy compared with standard step size strategies for subgradient methods. It is shown experimentally that our subgradient scheme achieves consistently better image registration than GC in terms of lower values both of the composite L-1-TV functional, and of its components, i.e., the L-1 distance of the images and the transformation smoothness TV, and yields visually acceptable results even in cases where the GC based algorithm fails. The new algorithm allows easy parallelization and can thus be sped

关键词： Convex optimization image registration subgradient algorithm total variation

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Stochastic perturbation of subgradient algorithm for nonconvex deep neural networks

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COMPUTATIONAL & APPLIED MATHEMATICS 2023年第4期42卷 1-26页

作者： El Mouatasim, A. de Cursi, J. E. Souza Ellaia, R. Ibnou Zohr Univ Math & Management Dept FPO Ouarzazate Morocco Normandie Univ Lab Mecan Normandie INSA Rouen Normandie 685 Ave Univ St-Etienne Rouvray Rouen France Mohammed V Univ Rabat Mohammadia Sch Engineers LERMA Ave Ibn Sina BP765 Rabat Morocco

Choosing a learning rate is a necessary part of any subgradient method optimization. With deeper models such as convolutional neural networks of image classification, fine-tuning the learning rate can quickly become tedious, and it does not always result in optimal convergence. In this work, we suggest a variation of the subgradient method in which the learning rate is updated by a control step in each iteration of each epoch. Stochastic Perturbation subgradient algorithm (SPSA) is our approach for tackling image classification issues with deep neural networks including convolutional neural networks. Used MNIST dataset, the numerical results reveal that our SPSA method is faster than Stochastic Gradient Descent and its variants with a fixed learning rate. However SPSA and convolutional neural network model improve the results of image classification including loss and accuracy.

关键词： subgradient algorithm Nonconvex nonsmooth optimization Stochastic perturbation Learning rate Image classification Deep neural networks and CNN

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Quantized subgradient algorithm and Data-Rate Analysis for Distributed Optimization

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2014年第4期1卷 380-392页

作者： Yi, Peng Hong, Yiguang Chinese Acad Sci Acad Math & Syst Sci Key Lab Syst & Control Beijing 100190 Peoples R China

In this paper, we consider quantized distributed optimization problems with limited communication capacity and time-varying communication topology. A distributed quantized subgradient algorithm is presented with quantized information exchange between agents. Based on a proposed encoder-decoder scheme and a zooming-in technique, the optimal solution can be obtained without any quantization errors. Moreover, we explore how to minimize the quantization level number for quantized distributed optimization problems. In fact, the optimization problem can be solved with five-level quantizers in the switching topology case, while it can be solved with three-level quantizers in the fixed topology case.

关键词： Data rate distributed optimization quantization subgradient algorithm

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A subgradient algorithm for Data-Rate Optimization in the Remote State Estimation Problem

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SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 2021年第4期20卷 2142-2173页

作者： Kawan, Christoph Hafstein, Sigurdur Giesl, Peter Ludwig Maximilians Univ Munchen Inst Informat Oettingenstr 67 D-80538 Munich Germany Univ Iceland Inst Sci Dunhagi 5 IS-107 Reykjavik Iceland Univ Sussex Dept Math Falmer BN1 9QH England

In the remote state estimation problem, an observer tries to reconstruct the state of a dynamical system at a remote location, where no direct sensor measurements are available. The observer only has access to information sent through a digital communication channel with a finite capacity. The recently introduced notion of restoration entropy provides a way to determine the smallest channel capacity above which an observer can be designed that observes the system without a degradation of the initial observation quality. In this paper, we propose a subgradient algorithm to estimate the restoration entropy via the computation of an appropriate Riemannian metric on the state space, which allows us to determine the approximate value of the entropy from the time-one map (in the discrete-time case) or the generating vector field (for ODE systems), respectively.

关键词： remote state estimation restoration entropy optimization on manifolds Lyapunov exponents subgradient algorithm adapted metrics

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AN EFFICIENT PROJECTED subgradient algorithm FOR BLIND IMAGE DECONVOLUTION USING AN L₁-TV COST FUNCTION

AN EFFICIENT PROJECTED SUBGRADIENT ALGORITHM FOR BLIND IMAGE...

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19th IEEE International Conference on Image Processing (ICIP)

作者： Xia, Wenyao Hatzinakos, Dimitrios Univ Toronto Dept Elect & Comp & Engn Toronto ON M5S 1A1 Canada

ISBN: (纸本)9781467325332;9781467325349

Traditional blind image iterative algorithms are designed for Gaussian noise by using the L-2-norm error term. For robustness against the influence of non-Gaussian noise, an efficient projected subgradient algorithm for blind image deconvolution is developed, based on a TV cost function with the L-1-norm error term. Because of using the subgradient technique, the proposed subgradient algorithm can minimize the L-1-TV cost function directly. By contrast, existing L-1 norm-based image restoration algorithms only minimize the approximate L-1 cost function and assume a known blur. Illustrative examples show that under suboptimal regularization parameters, the projected subgradient algorithm is efficient in producing better image estimate than two traditional blind image iterative algorithms in terms of both ISNR and perception.

关键词： Blind image deconvolution non-Gaussian noise L-1-TV cost function subgradient algorithm

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AN EFFICIENT PROJECTED subgradient algorithm FOR BLIND IMAGE DECONVOLUTION USING AN L_1-TV COST FUNCTION

AN EFFICIENT PROJECTED SUBGRADIENT ALGORITHM FOR BLIND IMAGE...

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IEEE International Conference on Image Processing

作者： Wenyao Xia Dimitrios Hatzinakos Department of Electrical and Computer and Engineering University of Toronto Canada

Traditional blind image iterative algorithms are designed for Gaussian noise by using the L_2-norm error term. For robustness against the influence of non-Gaussian noise, an efficient projected subgradient algorithm for blind image deconvolution is developed, based on a TV cost function with the L_1-norm error term. Because of using the subgradient technique, the proposed subgradient algorithm can minimize the L_1-TV cost function directly. By contrast, existing L_1 norm-based image restoration algorithms only minimize the approximate L_1 cost function and assume a known blur. Illustrative examples show that under suboptimal regularization parameters, the projected subgradient algorithm is efficient in producing better image estimate than two traditional blind image iterative algorithms in terms of both ISNR and perception.

关键词： Blind image deconvolution Non-Gaussian noise L_1-TV cost function subgradient algorithm

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A subgradient-Like algorithm for Solving Vector Convex Inequalities

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2014年第2期162卷 392-404页

作者： Bello Cruz, J. Y. Lucambio Perez, L. R. Univ Fed Goias BR-74001970 Goiania Go Brazil Univ Fed Goias Inst Matemat & Estat BR-74001970 Goiania Go Brazil

In this paper, we propose a strongly convergent variant of Robinson's subgradient algorithm for solving a system of vector convex inequalities in Hilbert spaces. The advantage of the proposed method is that it converges strongly, when the problem has solutions, under mild assumptions. The proposed algorithm also has the following desirable property: the sequence converges to the solution of the problem, which lies closest to the starting point and remains entirely in the intersection of three balls with radius less than the initial distance to the solution set.

关键词： Projection methods Strong convergence subgradient algorithm Vector convex functions

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Distributed subgradient Projection algorithm for Convex Optimization

Distributed Subgradient Projection Algorithm for Convex Opti...

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Ram, S. Sundhar Nedic, A. Veeravalli, V. V. Univ Illinois Urbana IL 61801 USA

ISBN: (纸本)9781424423538

We consider constrained minimization of a sum of convex functions over a convex and compact set, when each component function is known only to a specific agent in a time-varying peer to peer network. We study an iterative optimization algorithm in which each agent obtains a weighted average of its own iterate with the iterates of its neighbors, updates the average using the subgradient of its local function and then projects onto the constraint set to generate the new iterate. We obtain error bounds on the limit of the function value when a constant stepsize is used.

关键词： distributed optimization time-varying network subgradient algorithm

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