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ON THE BEHAVIOR OF THE DOUGLAS RACHFORD ALGORITHM FOR MINIMIZING A convex FUNCTION SUBJECT TO A LINEAR CONSTRAINT

SIAM JOURNAL ON optimization 2020年第3期30卷 2559-2576页

作者： Bauschke, Heinz H. Moursi, Walaa M. Univ British Columbia Math Kelowna BC V1V 1V7 Canada Univ Waterloo Dept Combinator & Optimizat Waterloo ON N2L 3G1 Canada

The Douglas Rachford algorithm (DRA) is a powerful optimization method for minimizing the sum of two convex (not necessarily smooth) functions. The vast majority of previous research dealt with the case when the sum has at least one minimizer. In the absence of minimizers, it was recently shown that for the case of two indicator functions, the DRA converges to a best approximation solution. In this paper, we present a new convergence result on the DRA applied to the problem of minimizing a convex function subject to a linear constraint. Indeed, a normal solution may be found even when the domain of the objective function and the linear subspace constraint have no point in common. As an important application, a new parallel splitting result is provided. We also illustrate our results through various examples.

关键词： convex optimization problem Douglas-Rachford splitting inconsistent constrained optimization least squares solution normal problem parallel splitting method projection operator proximal mapping

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A Multi-Step Reconfiguration Model for Active Distribution Network Restoration Integrating DG Start-Up Sequences

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2020年第4期11卷 2879-2888页

作者： Sekhavatmanesh, Hossein Cherkaoui, Rachid Ecole Polytech Fed Lausanne EPFL Power Syst Res Grp Lausanne Switzerland

The ever-increasing penetration of Distributed Generators (DGs) in distribution networks suggests to enable their potentials in better fulfilling the restoration objective. The objective of the restoration problem is to resupply the maximum energy of loads considering their priorities using minimum switching operations. Basically, it is desired to provide a unique configuration that is valid regarding the load and generation profiles along the entire restorative period. However, this unique configuration may not satisfy at the same time: I) the DG start-up requirements at the beginning of the restoration plan and II) the topological conditions that would allow the DG to provide later on the most efficient support for the supply of loads. Therefore, it is proposed in this article to allow a limited number of reconfiguration steps according to the DG start-up requirements. In addition, this article presents a novel formulation for the reconfiguration problem that accounts for partial restoration scenarios where the whole unsupplied area cannot be restored. The decision variables of the proposed multi-step restoration problem are: I) the line switching actions at each step of the reconfiguration process, II) the load switching actions during the whole restorative period and, III) the active/reactive power dispatch of DGs during the whole restorative period. A relaxed AC power flow formulation is integrated to the optimization problem in order to ensure the feasibility of the solution concerning the operational safety constraints. The overall model is formulated in terms of a mixed-integer second-order cone programming. Two simulation scenarios are studied in order to illustrate different features of the proposed strategy and to demonstrate its effectiveness particularly in the case of large-scale outages in distribution networks.

关键词： Switches optimization Load flow Load modeling Generators Safety convex optimization problem distribution network DG load breaker multi-step reconfiguration restoration service sectionalizing switch tie-switch

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Discrete Total Variation-Based Non-Local Means Filter for Denoising Magnetic Resonance Images

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JOURNAL OF INFORMATION TECHNOLOGY RESEARCH 2020年第4期13卷 14-31页

作者： Joshi, Nikita Jain, Sarika Agarwal, Amit Amity Univ Uttar Pradesh Amity Sch Engn & Technol Noida India Dr APJ Abdul Kalam Inst Technol Tanakpur Champawat India

Magnetic resonance (MR) images suffer from noise introduced by various sources. Due to this noise, diagnosis remains inaccurate. Thus, removal of noise becomes a very important task when dealing with MR images. In this paper, a denoising method has been discussed that makes use of non-local means filter and discrete total variation method. The proposed approach has been compared with other noise removal techniques like non-local means filter, anisotropic diffusion, total variation, and discrete total variation method, and it proves to be effective in reducing noise. The performance of various denoising methods is compared on basis of metrics such as peak signal-to-noise ratio (PSNR), mean square error (MSE), universal image quality index (UQI), and structure similarity index (SSIM) values. This method has been tested for various noise levels, and it outperformed other existing noise removal techniques, without blurring the image.

关键词： Antoni Buades convex optimization problem Discrete Total Variation Image Denoising Laurent Condat Noise Non-Local Means Regularization Parameter Search Window Similarity Window

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Service Restoration Model With Mixed-Integer Second-Order Cone Programming for Distribution Network With Distributed Generations

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IEEE TRANSACTIONS ON SMART GRID 2019年第4期10卷 4138-4150页

作者： Li, Yong Xiao, Juanxia Chen, Chun Tan, Yi Cao, Yijia Hunan Univ Coll Elect & Informat Engn Changsha 410082 Hunan Peoples R China

Fast and reliable service restoration strategy is necessary to restore as many out-of-service loads as possible in a short time. In this paper, a mixed-integer second-order cone programming formulation is proposed for service restoration of a distribution network with distributed generations (DGs). This formulation relaxes the original non-convex power flow equations into a conic quadratic format. The employment of conic relaxation is of great importance because it ensures the quality of the obtained solution. The service restoration is formulated as a multi-objective optimization problem considering the minimization of de-energized loads and total number of switching operations. Moreover, PQ and PV model of DGs are considered in this formulation. The proposed method is tested on the 33-bus system and the Taiwan Power Company 84-bus system to show its effectiveness.

关键词： convex optimization problem distribution network distributed generations mixed-integer second-order cone programming service restoration

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Design and Implementation of Adaptive Multi-Tap Analog Interference Canceller

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2019年第3期18卷 1698-1706页

作者： Zhang, Liyuan Ma, Meng Jiao, Bingli Peking Univ Sch Elect Engn & Comp Sci Beijing 100871 Peoples R China

Due to the severity of self-interferences, analog interference canceller is an essential part of a full duplex radio system. As the self-interference can potentially be even much stronger than the received signal, it must be meritoriously suppressed before analog-to-digital conversion. This paper is aimed to provide an optimal radio frequency domain multi-tap interference cancellation design. To this end, the following two key problems are addressed: the hardware design problem and the adaptive weight adjusting problem. For optimal hardware design, a trade-off between widening effective delay range and maximizing the minimum cancellation capability is formulated. The principles and guidelines for optimal solution and hardware parameter design are derived. We also formulate adaptive weight adjusting as a multi-dimensional optimization problem, which is proved to be non-convex while adjusting the attenuators and phase shifters independently. By using a coordinate transformation technique, it is then converted into a convex optimization problem, and a convergent iterative algorithm based on the gradient descent method is applied to obtain the global optimum. The hardware implementation and experimental results substantiated the effectiveness of the proposed principles and algorithms.

关键词： Full-duplex self-interference cancellation convex optimization problem iterative algorithm

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Weighted Sum Rate Maximization Under the Given PAPR Constraints for a Multi-user OFDM System

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WIRELESS PERSONAL COMMUNICATIONS 2019年第1期109卷 127-137页

作者： Falahati, Abolfazl Anarakifirooz, Elhamsadat Univ Sci & Technol Dept Elect Engn Tehran Iran

Orthogonal frequency division multiplexing (OFDM) is proved to be the best candidate to support the colossal increase in mobile users and their required high rate of transmission in frequency selective fading environments, where the inter-symbol interference is at highest. In an OFDM system, when the sinusoidal signals of the subcarriers are added constructively, the peak to average power ratio (PAPR) becomes very large causing major drawbacks for multicarrier signaling. Earlier efforts to address this problem have been mainly concentrated on the reduction of signal PAPR and various methods of achieving linear and efficient power amplification. However, all the deployed techniques suffer from different ambiguities such as high distortion, complexity, computational time, memory requirements, and above all, the data rate loss. This manuscript is mainly aimed at solving a convex optimization problem in which power and radio resources in an OFDM system are allocated among different subcarriers and users in order to, maximize the weighted sum rate for different users considering total power and PAPR limitations.

关键词： Orthogonal frequency division multiplexing (OFDM) Peak to average power ratio (PAPR) convex optimization problem Power and radio resources

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A Min-Max selector controller for turbofan engines with improvement of limit management and low computational burden

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2019年第1期41卷 36-44页

作者： Imani, Amin Montazeri-Gh, Morteza Iran Univ Sci & Technol Sch Mech Engn Syst Simulat & Control Lab Tehran *** Iran

Recent studies show that there is no guarantee for conventional Min-Max structure containing linear compensators to keep engine limitations in transient state, while limit violation can make dangerous events. Careful analysis indicates that despite the design of limitation loops overshoot-free to reduce the possibility of limit violation, exceeding the limits can occur for some variables affected by engine acceleration or deceleration, when other loop controllers are active. In this study, the limit values of these variables are taken into account in controller design of other loops using state feedback techniques and convex optimization problems, and their dynamic compensators are removed from the Min-Max structure. Thus, in addition to improvement of Min-Max limit protection, computational burden also decreases owing to loop reduction. The condition for limit protection in steady state and thrust tracking assurance is also specified. Simulations carried out with linear and nonlinear turbofan engine model show efficient performance of the proposed methodology in comparison with traditional Min-Max and Min-Max/sliding mode control (SMC) approaches.

关键词： Nonlinear turbofan engine model Min-Max structure limit management state feedback convex optimization problem

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convex formulation of confidence level optimization of DG affine reactive power controllers in distribution grids

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ELECTRIC POWER SYSTEMS RESEARCH 2020年第0期180卷 106132-000页

作者： Buire, Jerome Dieulot, Jean-Yves Colas, Frederic Guillaud, Xavier De Alvaro, Leticia Univ Lille Arts & Metiers Paris Tech Cent Lille HEIEA 2697L2EP F-59000 Lille France Univ Lille CNRS Cent Lille CRIStALUMR 9189 F-59000 Lille France Enedis F-92079 Paris France

Volatile productions and consumptions generate a stochastic behavior of distribution grids and make its supervision difficult to achieve. Usually, the Distributed Generators reactive powers are adjusted to perform decentralized voltage control. Industrial controllers are generally equipped with a local affine feedback law, which settings are tuned at early stage using local data. A centralized and more efficient tuning method should aim to maximize the probability that all the node voltages of distribution grids remain within prescribed bounds. When the characteristics of the stochastic power forecasts are known, the centralized algorithm allows to update the settings on a regular time basis. However, the method requires to solve stochastic optimization problem. Assuming that stochastic variables have Gaussian distributions, a procedure is given which guarantees the convergence of the stochastic optimization. convex problems drastically reduce the difficulty and the computational time required to reach the global minimum, compared to nonconvex optimal power flow problems. The linear controllers with optimized parameters are compared to traditional control laws using simulations of a real distribution grid model. The results show that the algorithm is reliable and moreover fast enough. Hence, the proposed method can be used to update periodically the control parameters.

关键词： Confidence level optimization Control tuning Distribution network Stochastic power flow convex optimization problem Fractional programming problem

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Three-term conjugate gradient method for the convex optimization problem over the fixed point set of a nonexpansive mapping

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APPLIED MATHEMATICS AND COMPUTATION 2011年第13期217卷 6315-6327页

作者： Iiduka, Hideaki Kyushu Inst Technol Network Design Res Ctr Chiyoda Ku Tokyo 1000011 Japan

Many constrained sets in problems such as signal processing and optimal control can be represented as a fixed point set of a certain nonexpansive mapping, and a number of iterative algorithms have been presented for solving a convex optimization problem over a fixed point set. This paper presents a novel gradient method with a three-term conjugate gradient direction that is used to accelerate conjugate gradient methods for solving unconstrained optimization problems. It is guaranteed that the algorithm strongly converges to the solution to the problem under the standard assumptions. Numerical comparisons with the existing gradient methods demonstrate the effectiveness and fast convergence of this algorithm. (C) 2011 Elsevier Inc. All rights reserved.

关键词： convex optimization problem Fixed point set convex function Nonexpansive mapping Conjugate gradient method Three-term conjugate gradient method

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Mode Filtering with a Small Horizontal Line Array 10

Mode Filtering with a Small Horizontal Line Array

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10th International Conference on Wireless Communications and Signal Processing (WCSP)

作者： Zhang, Yifeng Wang, Jinjin Liang, Guolong Shi, Zhibo Harbin Engn Univ Underwater Acoust Coll Harbin Heilongjiang Peoples R China

ISBN: (纸本)9781538661192

Mode filtering is a key procedure in passive localization or source depth discrimination. Since the horizontal line array (HLA) lacks sampling of modes in depth direction, the orthogonality of modes can't be utilized in mode filtering with a HLA. Thus, the mode filtering with a HLA, especially with a small HLA is generally a difficult problem. In this paper, we focus on the mode filtering with a small HLA, which can be applied to the passive localization or source depth discrimination with a small HLA. Firstly, the pressure received on the HLA is describe by normal mode model, and several classical mode filters are introduced. Then considering the modal amplitudes are corresponding to the wavenumbers, we regard the mode filtering as generalized beamforming, which is performed in the wavenumber domain. Through constraining the maximum side lobe minimum, the modal amplitudes are beamformed. Finally, the performance of the proposed mode filter is evaluated relative to other methods in Monte Carlo simulation.

关键词： Mode filtering Small horizontal line array (HLA) convex optimization problem

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