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Dynamics of the Douglas-Rachford Method for Ellipses and p-Spheres

SET-VALUED AND VARIATIONAL ANALYSIS 2018年第2期26卷 385-403页

作者： Borwein, Jonathan M. Lindstrom, Scott B. Sims, Brailey Schneider, Anna Skerritt, Matthew P. Univ Newcastle CARMA Newcastle NSW Australia Univ Bundeswehr Munchen Neubiberg Germany

We expand upon previous work that examined the behavior of the iterated Douglas-Rachford method for a line and a circle by considering two generalizations:that of a line and an ellipse and that of a line together with a p-sphere. With computer assistance we discover a beautiful geometry that illustrates phenomena which may affect the behavior of the iterates by slowing or inhibiting convergence for feasible cases. We prove local convergence near feasible points, and-seeking a better understanding of the behavior-we employ parallelization in order to study behavior graphically. Motivated by the computer-assisted discoveries, we prove a result about behavior of the method in infeasible cases.

关键词： Douglas-Rachford Feasibility projection algorithms Iterative methods Discrete dynamical systems

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AN EFFICIENT ALGORITHM FOR RECONSTRUCTION OF SPECT IMAGES IN THE PRESENCE OF SPATIALLY VARYING ATTENUATION

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 1985年第2期32卷 1190-1197页

作者： ZEEBERG, BR SOUCAILLE, JF CARSON, R BACHARACH, S GREEN, MV LARSON, SM Department of Nuclear Medicine National Institutes of Health DHHS Bethesda MD USA

An algorithm is presented which permits the reconstruction of SPECT images in the presence of spatially varying attenuation. The algorithm considers the spatially variant attenuation as a perturbation of the constant attenuation case and computes a reconstructed image and a correction image to estimate the effects of this perturbation. The corrected image will be computed from these two images and is of comparable quality both visually and quantitatively to those simulated for zero or constant attenuation taken as standard reference images. In addition, the algorithm is time efficient, in that the time required is approximately 2.5 times that for a standard convolution-back projection algorithm.

关键词： Attenuation Image reconstruction Filtering Least squares approximation Least squares methods Iterative methods Iterative algorithms Nuclear medicine projection algorithms Reconstruction algorithms

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Storage and Transmission Capacity Requirements of a Remote Solar Power Generation System

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IEEE SYSTEMS JOURNAL 2022年第2期16卷 3175-3178页

作者： Chen, Yue Wei, Wei Wang, Cheng Shafie-khah, Miadreza Catalao, Joao P. S. Chinese Univ Hong Kong Dept Mech & Automat Engn Hong Kong Peoples R China Tsinghua Univ Dept Elect Engn State Key Lab Power Syst Beijing 100084 Peoples R China North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Beijing 102206 Peoples R China Univ Vaasa Sch Technol & Innovat Vaasa 65200 Finland Univ Porto Fac Engn P-4200465 Porto Portugal INESC TEC P-4200465 Porto Portugal

Large solar power stations are usually located in remote areas and connect to the main grid via a long transmission line. The energy storage unit is deployed locally with the solar plant to smooth its output. Capacities of the grid-connection transmission line and the energy storage unit have a significant impact on the utilization rate of solar energy, as well as the investment cost. This article characterizes the feasible set of capacity parameters under a given solar spillage rate and a fixed investment budget. A linear programming-based projection algorithm is proposed to obtain such a feasible set, offering valuable references for system planning and policy making.

关键词： Renewable energy sources Energy storage Power transmission lines Costs projection algorithms Planning Investment Energy storage unit polyhedral projection algorithm renewable power spillage transmission line

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Membership set identification with periodic inputs and orthonormal regressors

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SIGNAL PROCESSING 2006年第12期86卷 3778-3786页

作者： Akcay, Huseyin At, Nuray Anadolu Univ Dept Elect & Elect Engn TR-26470 Eskisehir Turkey

In this paper, we study the central and the projection algorithms in membership-set estimation with periodic input signals and orthonormal basis functions for the special case that the number of the estimated parameters equals the input period (or overparameterized model structures). First, we derive explicit formulae for a central algorithm and the diameter of the membership set. Then, we characterize the set of all projection algorithms. (c) 2006 Elsevier B.V. All rights reserved.

关键词： identification membership set orthonormal basis functions periodic inputs central algorithms projection algorithms

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On the regularity condition in a convex feasibility problem

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2009年第5期70卷 1923-1928页

作者： Maruster, Stefan Popirlan, Cristina W Univ Timisoara Timisoara Romania Univ Craiova Craiova Romania

The regularity properties of a family of closed convex sets with nonempty intersection are investigated in the frame of a real Hilbert space. The significant role of these properties in solving convex feasibility prob... 详细信息

关键词： Convex feasibility problem projection algorithms Regularity properties

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Robust Online Multiuser Detection: A Hybrid Model-Data Driven Approach

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2023年 71卷 2103-2117页

作者： Awan, Daniyal Amir Cavalcante, Renato Luis Garrido Yukawa, Masahiro Stanczak, Slawomir Fraunhofer Inst Nachrichtentech n Heinrich Hertz Inst HHI D-10587 Berlin Germany Wireless Commun & Networks Fraunhofer Inst Nachrichtentechn Heinrich Hertz Inst HHI D-10587 Berlin Germany Keio Univ Elect & Elect Engn Yokohama 2238522 Japan

We study the problem of robust online multiuser detection in the context of non-orthogonal multiple access. The optimal multiuser detector (in terms of the uncoded bit error rate) is the nonlinear maximum a posteriori (MAP) filter. Learning good nonlinear functions of this type (e.g., with deep neural networks) typically requires a large number of training samples and complicated signal processing, which poses a fundamental problem in dynamic wireless environments. Furthermore, compared with linear approaches, nonlinear filters are generally less robust against changes in the environment. To overcome these problems, we first show that the optimal MAP filter belongs to reproducing kernel Hilbert spaces (RKHSs) associated with Gaussian kernels whose widths satisfy a condition related to the standard deviation of the receiver noise. Second, we show how to approximate the optimal MAP filter with a computationally simple signal processing algorithm using a relatively small number of training samples. Third, to make the filter robust against changes in the wireless environment, we design a partially linear filter in the sum of an RKHS containing the MAP filter and an RKHS of a linear kernel. Finally, based on this partially linear design, we propose a multiuser detection framework that, in contrast to some state-of-the-art approaches, has the following desired features: (i) it has low complexity;(ii) it can work with small sample sets;(iii) it shows better robustness than a purely nonlinear receiver;and (iv) it does not require user parameter estimation (e.g., channels), which is prone to errors and may not be possible in certain scenarios.

关键词： NOMA multiuser detection nonlinear filters machine learning projection algorithms

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Decoding Nonbinary LDPC Codes via Proximal-ADMM Approach

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IEEE TRANSACTIONS ON INFORMATION THEORY 2022年第9期68卷 5730-5746页

作者： Wang, Yongchao Bai, Jing Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Peoples R China Shijiazhuang Tiedao Univ Sch Informat Sci & Technol Shijiazhuang 050043 Hebei Peoples R China

In this paper, we focus on decoding nonbinary low-density parity-check (LDPC) codes in Galois fields of characteristic two via the proximal alternating direction method of multipliers (proximal-ADMM). By exploiting Flanagan/Constant-Weighting embedding techniques and the decomposition technique based on three-variables parity-check equations, two efficient proximal-ADMM decoders for nonbinary LDPC codes are proposed. We show that both of them are theoretically guaranteed convergent to some stationary point of the decoding model and either of their computational complexities in each proximal-ADMM iteration scales linearly with LDPC code's length and the size of the considered Galois field. Moreover, the decoder based on the Constant-Weight embedding technique satisfies the favorable property of codeword symmetry. Simulation results demonstrate their effectiveness in comparison with state-of-the-art LDPC decoders.

关键词： Maximum likelihood decoding Mathematical models Iterative decoding Linear matrix inequalities projection algorithms Heuristic algorithms Convergence Nonbinary low-density parity-check (LDPC) codes Galois fields of characteristic two proximal alternating direction method of multipliers (proximal-ADMM) quadratic programming (QP)

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SOME EFFICIENT algorithms FOR A CLASS OF ABSTRACT OPTIMIZATION PROBLEMS ARISING IN OPTIMAL CONTROL

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1969年第6期AC14卷 640-+页

作者： BARR, RO GILBERT, EG Department of Electrical Engineering and Systems Science Michigan State University East Lansing MI USA Computer Information and Control Engineering Program University of Michigan Ann Arbor MI USA

Three abstract optimization problems are presented along with doubly iterative algorithms for their numerical solution. These algorithms are generalizations of particular algorithms described by Barr and Gilbert [19], [21] and Fujisawa and Yasuda [22]. The supporting theory is fully developed along with proofs of convergence. Practical aspects of computations are considered and procedures which insure rapid convergence are discussed. Two applications to discrete-time optimal control problems are described.

关键词： Optimal control Iterative algorithms projection algorithms Dynamic programming Nonlinear equations Gradient methods Functional programming Boundary conditions Military computing Convergence of numerical methods

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Efficient computation of the Hausdorff distance between polytopes by exterior random covering

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2005年第2期30卷 161-194页

作者： Llanas, B Univ Politecn Madrid Dept Matemat Aplicada ETSI Caminos E-28040 Madrid Spain

In this paper, a simple yet efficient randomized algorithm (Exterior Random Covering) for finding the maximum distance from a point set to an arbitrary compact set in R-d is presented. This algorithm can be used for a... 详细信息

关键词： Hausdorff distance maximum distance polytopes polyhedra projection algorithms Lipschitz random covering

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Localization of a Coherent Acoustic Source in a Shallow-Water Channel Using the Partially Calibrated Adaptive Antenna Array

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RADIOPHYSICS AND QUANTUM ELECTRONICS 2016年第2期59卷 88-96页

作者： Sazontov, A. G. Smirnov, I. P. Chashchin, A. S. Russian Acad Sci Inst Appl Phys Moscow 117901 Russia NI Lobachevsky State Univ Nizhny Novgorod Nizhnii Novgorod Russia

We consider the problem of determining the location of a coherent acoustic source in a shallowwater channel using a partially calibrated antenna array. To solve this problem, we develop a reduced-rank stable projection algorithm, which is the generalization of the RARE method to the case of signal reception under the conditions of incomplete information on the propagation medium. The results of experimental validation of the proposed approach, which show its efficiency under the conditions of an actual shallow-water area, are presented.

关键词： Calibration signal reception acoustic radiators propagation medium Generalization Antenna arrays adaptive antenna arrays projection algorithms

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