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1

Dong, Zhengshan, Geng Lin, and Niandong Chen. "An Inexact Penalty Decomposition Method for Sparse Optimization." Computational Intelligence and Neuroscience 2021 (July 14, 2021): 1–8. http://dx.doi.org/10.1155/2021/9943519.

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The penalty decomposition method is an effective and versatile method for sparse optimization and has been successfully applied to solve compressed sensing, sparse logistic regression, sparse inverse covariance selection, low rank minimization, image restoration, and so on. With increase in the penalty parameters, a sequence of penalty subproblems required being solved by the penalty decomposition method may be time consuming. In this paper, an acceleration of the penalty decomposition method is proposed for the sparse optimization problem. For each penalty parameter, this method just finds so
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Wang, Yuanxin. "An Adaptive Variational Mode Decomposition Technique with Differential Evolution Algorithm and Its Application Analysis." Shock and Vibration 2021 (November 11, 2021): 1–5. http://dx.doi.org/10.1155/2021/2030128.

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Variational mode decomposition is an adaptive nonrecursive signal decomposition and time-frequency distribution estimation method. The improper selection of the decomposition number will cause under decomposition or over decomposition, and the improper selection of the penalty factor will affect the bandwidth of modal components, so it is very necessary to look for the optimal parameter combination of the decomposition number and the penalty factor of variational mode decomposition. Hence, differential evolution algorithm is used to look for the optimization combination of the decomposition nu
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3

Lu, Zhaosong, and Yong Zhang. "Sparse Approximation via Penalty Decomposition Methods." SIAM Journal on Optimization 23, no. 4 (2013): 2448–78. http://dx.doi.org/10.1137/100808071.

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4

Lu, Zhaosong, Yong Zhang, and Xiaorui Li. "Penalty decomposition methods for rank minimization." Optimization Methods and Software 30, no. 3 (2014): 531–58. http://dx.doi.org/10.1080/10556788.2014.936438.

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5

Xu, Huaqing, Tieding Lu, Jean-Philippe Montillet, and Xiaoxing He. "An Improved Adaptive IVMD-WPT-Based Noise Reduction Algorithm on GPS Height Time Series." Sensors 21, no. 24 (2021): 8295. http://dx.doi.org/10.3390/s21248295.

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To improve the reliability of Global Positioning System (GPS) signal extraction, the traditional variational mode decomposition (VMD) method cannot determine the number of intrinsic modal functions or the value of the penalty factor in the process of noise reduction, which leads to inadequate or over-decomposition in time series analysis and will cause problems. Therefore, in this paper, a new approach using improved variational mode decomposition and wavelet packet transform (IVMD-WPT) was proposed, which takes the energy entropy mutual information as the objective function and uses the grass
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Lee, Ju Hwan and 윤자영. "Wage Penalty and Decomposition of Care Employment." Korean Journal of Social Welfare Studies 46, no. 4 (2015): 33–57. http://dx.doi.org/10.16999/kasws.2015.46.4.33.

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7

Wang, Caihua, Juan Liu, Wenwen Min, and Aiping Qu. "A Novel Sparse Penalty for Singular Value Decomposition." Chinese Journal of Electronics 26, no. 2 (2017): 306–12. http://dx.doi.org/10.1049/cje.2017.01.025.

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8

Lazarov, Raytcho D., Stanimire Z. Tomov, and Panayot S. Vassilevski. "Interior Penalty Discontinuous Approximations of Elliptic Problems." Computational Methods in Applied Mathematics 1, no. 4 (2001): 367–82. http://dx.doi.org/10.2478/cmam-2001-0024.

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AbstractThis paper studies an interior penalty discontinuous approximation of elliptic problems on nonmatching grids. Error analysis, interface domain decomposition type preconditioners, as well as numerical results illustrating both discretization errors and condition number estimates of the problem and reduced forms of it are presented.
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9

Ouellet, Yanick, and Claude-Guy Quimper. "The SoftCumulative Constraint with Quadratic Penalty." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 4 (2022): 3813–20. http://dx.doi.org/10.1609/aaai.v36i4.20296.

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The Cumulative constraint greatly contributes to the success of constraint programming at solving scheduling problems. The SoftCumulative, a version of the Cumulative where overloading the resource incurs a penalty is, however, less studied. We introduce a checker and a filtering algorithm for the SoftCumulative, which are inspired by the powerful energetic reasoning rule for the Cumulative. Both algorithms can be used with classic linear penalty function, but also with a quadratic penalty function, where the penalty of overloading the resource increases quadratically with the amount of the ov
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10

Zhao, Ming-Min, Qingjiang Shi, Yunlong Cai, Min-Jian Zhao, and Quan Yu. "Decoding Binary Linear Codes Using Penalty Dual Decomposition Method." IEEE Communications Letters 23, no. 6 (2019): 958–62. http://dx.doi.org/10.1109/lcomm.2019.2911277.

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11

Wang, Hongjun, Xiang Zhang, Zhengbo Wang, and Shucong Liu. "Impact Load Sparse Recognition Method Based on Mc Penalty Function." Applied Sciences 12, no. 16 (2022): 8147. http://dx.doi.org/10.3390/app12168147.

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The rotor system is an important part of large-scale rotating machinery. Bearings, as a key component of the rotor system, play a vital role in the healthy operation of the rotor system. The bearings operate under harsh conditions such as high temperature, high pressure, and high speed. They are complex and extremely prone to failure, especially when the bearing is affected by impact load, which seriously affects the remaining service life of the bearing. Uneven bearing friction, caused by the impact, is one of the main factors that cause premature failure of the bearing. The early identificat
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12

Dong, Zhengshan, and Wenxing Zhu. "An improvement of the penalty decomposition method for sparse approximation." Signal Processing 113 (August 2015): 52–60. http://dx.doi.org/10.1016/j.sigpro.2015.01.012.

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13

Liu, Jian, Yuhu Cheng, Xuesong Wang, and Xiaoluo Cui. "Supervised Penalty Matrix Decomposition for Tumor Differentially Expressed Genes Selection." Chinese Journal of Electronics 27, no. 4 (2018): 845–51. http://dx.doi.org/10.1049/cje.2017.09.023.

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14

Tokareva, O. N. "Two-level decomposition in sequential quadratic programming with penalty functions." Cybernetics 26, no. 6 (1991): 891–902. http://dx.doi.org/10.1007/bf01069495.

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15

Chen, Xieqi, Jianhui Lin, Hang Jin, Andy Tan, and Lei Yan. "Acoustics Source Identification of Diesel Engines Based on Variational Mode Decomposition, Fast Independent Component Analysis, and Hilbert Transformation." Shock and Vibration 2021 (January 20, 2021): 1–18. http://dx.doi.org/10.1155/2021/8832932.

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Diesel engines are widely used in railway systems, particularly in freight trains. Despite their high efficiency in energy conversion, they usually generate high levels of acoustics pollution during operation. In order to mitigate this problem, a series of active/passive acoustics control methods are used to reduce noise. Most of these methods are only effective if the prior knowledge of sources is given. In other words, it is essential to recognize the acoustics source. Variational mode decomposition (VMD) is a signal processing method that enhances the signal corrupted by background noise. H
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16

Rolli, Fernando, João Fradinho, Alessandro Giorgetti, Paolo Citti, and Gabriele Arcidiacono. "Axiomatic decomposition of a zero-sum game: the penalty shoot-out case." MATEC Web of Conferences 223 (2018): 01005. http://dx.doi.org/10.1051/matecconf/201822301005.

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The game of soccer has offered matter of wide scientific analysis about the effective application of the game theory in real-life. The field observations have often detected divergent behaviors from theoretical predictions. The basic problem comes from the fact that it is difficult to build scientific models reflecting reality as closely as possible. Axiomatic Design offers us a powerful tool of rational decomposition of a real and complex issue into elementary components. Independence Axiom guarantees that game decomposition will define a set of elementary actions logically consistent and fre
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17

He, Zhitao, Haiyang Zhang, Jun Wang, Xin Jin, Song Gao, and Jing Pang. "BP-AdaBoost Algorithm Based on Variational Mode Decomposition Optimized by Envelope Entropy for Diagnosing the Working Conditions of a Slideway Seedling-Picking Mechanism." Applied Engineering in Agriculture 37, no. 4 (2021): 665–75. http://dx.doi.org/10.13031/aea.14124.

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Highlights A method of monitoring the working conditions of a slideway seedling-picking mechanism based on variational mode decomposition (VMD), envelope entropy, and energy entropy is proposed. Based on the criterion of envelope entropy minimization, the combination of the decomposition layer number and penalty factor in VMD is optimized to yield a satisfactory decomposition effect of the analyzed vibration signal. The BP-AdaBoost algorithm is used to improve the working condition classification performance for the slideway seedling-picking mechanism. The working-condition identification effe
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18

Li, Ziyue, Nurettin Dorukhan Sergin, Hao Yan, Chen Zhang, and Fugee Tsung. "Tensor Completion for Weakly-Dependent Data on Graph for Metro Passenger Flow Prediction." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 4804–10. http://dx.doi.org/10.1609/aaai.v34i04.5915.

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Low-rank tensor decomposition and completion have attracted significant interest from academia given the ubiquity of tensor data. However, low-rank structure is a global property, which will not be fulfilled when the data presents complex and weak dependencies given specific graph structures. One particular application that motivates this study is the spatiotemporal data analysis. As shown in the preliminary study, weakly dependencies can worsen the low-rank tensor completion performance. In this paper, we propose a novel low-rank CANDECOMP / PARAFAC (CP) tensor decomposition and completion fr
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19

Qiao, Junfei, Hongbiao Zhou, Cuili Yang, and Shengxiang Yang. "A decomposition-based multiobjective evolutionary algorithm with angle-based adaptive penalty." Applied Soft Computing 74 (January 2019): 190–205. http://dx.doi.org/10.1016/j.asoc.2018.10.028.

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20

Shi, Qingjiang, Mingyi Hong, Xiao Fu, and Tsung-Hui Chang. "Penalty Dual Decomposition Method for Nonsmooth Nonconvex Optimization—Part II: Applications." IEEE Transactions on Signal Processing 68 (2020): 4242–57. http://dx.doi.org/10.1109/tsp.2020.3001397.

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21

Jin, Zheng-Fen, Zhongping Wan, Xiaoke Zhao, and Yunhai Xiao. "A penalty decomposition method for rank minimization problem with affine constraints." Applied Mathematical Modelling 39, no. 16 (2015): 4859–70. http://dx.doi.org/10.1016/j.apm.2015.03.054.

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22

Rahman, Mustafizur, and Md Al-Hasan. "Male–Female Wage Gap and Informal Employment in Bangladesh: A Quantile Regression Approach." South Asia Economic Journal 20, no. 1 (2019): 106–23. http://dx.doi.org/10.1177/1391561418824477.

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This article undertakes an examination of Bangladesh’s latest available Quarterly Labour Force Survey 2015–2016 data to draw in-depth insights on gender wage gap and wage discrimination in Bangladesh labour market. The mean wage decomposition shows that on average a woman in Bangladesh earns 12.2 per cent lower wage than a man, and about half of the wage gap can be explained by labour market discrimination against women. Quantile counterfactual decomposition shows that women are subject to higher wage penalty at the lower deciles of the wage distribution with the wage gap varying between 8.3 p
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23

Rasti, Behnood, Pedram Ghamisi, and Magnus Ulfarsson. "Hyperspectral Feature Extraction Using Sparse and Smooth Low-Rank Analysis." Remote Sensing 11, no. 2 (2019): 121. http://dx.doi.org/10.3390/rs11020121.

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In this paper, we develop a hyperspectral feature extraction method called sparse and smooth low-rank analysis (SSLRA). First, we propose a new low-rank model for hyperspectral images (HSIs) where we decompose the HSI into smooth and sparse components. Then, these components are simultaneously estimated using a nonconvex constrained penalized cost function (CPCF). The proposed CPCF exploits total variation penalty, ℓ 1 penalty, and an orthogonality constraint. The total variation penalty is used to promote piecewise smoothness, and, therefore, it extracts spatial (local neighborhood) informati
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24

Bi, Shujun, Xiaolan Liu, and Shaohua Pan. "Exact Penalty Decomposition Method for Zero-Norm Minimization Based on MPEC Formulation." SIAM Journal on Scientific Computing 36, no. 4 (2014): A1451—A1477. http://dx.doi.org/10.1137/110855867.

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25

Yang, Shengxiang, Shouyong Jiang, and Yong Jiang. "Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes." Soft Computing 21, no. 16 (2016): 4677–91. http://dx.doi.org/10.1007/s00500-016-2076-3.

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26

Pinar, Mustafa C., and Stavros A. Zenios. "Parallel Decomposition of Multicommodity Network Flows Using a Linear-Quadratic Penalty Algorithm." ORSA Journal on Computing 4, no. 3 (1992): 235–49. http://dx.doi.org/10.1287/ijoc.4.3.235.

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27

Zhao, Ming-Min, Qingjiang Shi, Yunlong Cai, Min-Jian Zhao, and Yongjie Li. "Distributed Penalty Dual Decomposition Algorithm for Optimal Power Flow in Radial Networks." IEEE Transactions on Power Systems 35, no. 3 (2020): 2176–89. http://dx.doi.org/10.1109/tpwrs.2019.2952433.

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28

Liu, Qiegen, Biao Xiong, and Minghui Zhang. "Adaptive Sparse Norm and Nonlocal Total Variation Methods for Image Smoothing." Mathematical Problems in Engineering 2014 (2014): 1–18. http://dx.doi.org/10.1155/2014/426125.

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In computer vision and graphics, it is challenging to decompose various texture/structure patterns from input images. It is well recognized that how edges are defined and how this prior information guides smoothing are two keys in determining the quality of image smoothing. While many different approaches have been reported in the literature, sparse norm and nonlocal schemes are two promising tools. In this study, by integrating a texture measure as the spatially varying data-fidelity/smooth-penalty weight into the sparse norm and nonlocal total variation models, two new methods are presented
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29

Yu, Chengbo, and Youyu Mi. "Optimised VMD based on Improved Grey Wolf for Human Pulse Wave Characterisation." Journal of Physics: Conference Series 2356, no. 1 (2022): 012023. http://dx.doi.org/10.1088/1742-6596/2356/1/012023.

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To address the difficulty in determining the penalty factor α mode and number K for the Variational Mode Decomposition (VMD) human pulse wave signal, which makes it difficult to extract and analyse its features accurately, an Improved Grey Wolf Optimization (IGWO) method is proposed to optimise the VMD. In this paper, the optimal modal number K and penalty factor α in the VMD are determined by IGWO using Minimum Average Mutual Information (MAMI) as the fitness function. The proposed method is used to completely decompose the pulse wave into K Intrinsic Mode Functions (IMF), and the marginal sp
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30

Liang, Tao, and Hao Lu. "A Novel Method Based on Multi-Island Genetic Algorithm Improved Variational Mode Decomposition and Multi-Features for Fault Diagnosis of Rolling Bearing." Entropy 22, no. 9 (2020): 995. http://dx.doi.org/10.3390/e22090995.

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Aiming at the problem that it is difficult to extract fault features from the nonlinear and non-stationary vibration signals of wind turbine rolling bearings, which leads to the low diagnosis and recognition rate, a feature extraction method based on multi-island genetic algorithm (MIGA) improved variational mode decomposition (VMD) and multi-features is proposed. The decomposition effect of the VMD method is limited by the number of decompositions and the selection of penalty factors. This paper uses MIGA to optimize the parameters. The improved VMD method is used to decompose the vibration s
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Kong Deming, 孔德明, 张春祥 Zhang Chunxiang, 崔耀耀 Cui Yaoyao, 李雨蒙 Li Yumeng, and 王书涛 Wang Shutao. "Detection of Oil Species in Mixed Oil Based on Alternating Penalty Trilinear Decomposition." Acta Optica Sinica 38, no. 11 (2018): 1130005. http://dx.doi.org/10.3788/aos201838.1130005.

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Zhao, Jingtao, Suping Peng, and Wenfeng Du. "Seismic small-scale discontinuity sparsity-constraint inversion method using a penalty decomposition algorithm." Journal of Geophysics and Engineering 13, no. 1 (2016): 109–15. http://dx.doi.org/10.1088/1742-2132/13/1/109.

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Murata, Naoki, Shoichi Koyama, Norihiro Takamune, and Hiroshi Saruwatari. "Sparse Representation Using Multidimensional Mixed-Norm Penalty With Application to Sound Field Decomposition." IEEE Transactions on Signal Processing 66, no. 12 (2018): 3327–38. http://dx.doi.org/10.1109/tsp.2018.2830318.

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34

Cai, Gaigai, Ivan W. Selesnick, Shibin Wang, Weiwei Dai, and Zhongkui Zhu. "Sparsity-enhanced signal decomposition via generalized minimax-concave penalty for gearbox fault diagnosis." Journal of Sound and Vibration 432 (October 2018): 213–34. http://dx.doi.org/10.1016/j.jsv.2018.06.037.

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35

Xia, A.-Lin, Hai-Long Wu, Shu-Fang Li, Shao-Hua Zhu, Le-Qian Hu, and Ru-Qin Yu. "Alternating penalty quadrilinear decomposition algorithm for an analysis of four-way data arrays." Journal of Chemometrics 21, no. 3-4 (2007): 133–44. http://dx.doi.org/10.1002/cem.1051.

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36

Shi, Yan, Zhou Chen, and Chang-Hong Liang. "An interior penalty Galerkin domain decomposition method based on high-order basis function." Microwave and Optical Technology Letters 57, no. 8 (2015): 1961–65. http://dx.doi.org/10.1002/mop.29235.

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37

Wu, Shuonan, Shihua Gong, and Jinchao Xu. "Interior penalty mixed finite element methods of any order in any dimension for linear elasticity with strongly symmetric stress tensor." Mathematical Models and Methods in Applied Sciences 27, no. 14 (2017): 2711–43. http://dx.doi.org/10.1142/s0218202517500567.

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We propose two classes of mixed finite elements for linear elasticity of any order, with interior penalty for nonconforming symmetric stress approximation. One key point of our method is to introduce some appropriate nonconforming face-bubble spaces based on the local decomposition of discrete symmetric tensors, with which the stability can be easily established. We prove the optimal [Formula: see text]-error estimate for displacement and optimal [Formula: see text] error estimate for stress by adding an interior penalty term. The elements are easy to be implemented thanks to the explicit form
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Yang, Jingzong, Chengjiang Zhou, and Xuefeng Li. "Research on Fault Feature Extraction Method Based on Parameter Optimized Variational Mode Decomposition and Robust Independent Component Analysis." Coatings 12, no. 3 (2022): 419. http://dx.doi.org/10.3390/coatings12030419.

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The variational mode decomposition mode (VMD) has a reliable mathematical derivation and can decompose signals adaptively. At present, it has been widely used in mechanical fault diagnosis, financial analysis and prediction, geological signal analysis, and other fields. However, VMD has the problems of insufficient decomposition and modal aliasing due to the unclear selection method of modal component k and penalty factor α. Therefore, it is difficult to ensure the accuracy of fault feature extraction and fault diagnosis. To effectively extract fault feature information from bearing vibration
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Shao, Yang, Zhen Peng, Kheng Hwee Lim, and Jin-Fa Lee. "Non-conformal domain decomposition methods for time-harmonic Maxwell equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2145 (2012): 2433–60. http://dx.doi.org/10.1098/rspa.2012.0028.

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We review non-conformal domain decomposition methods (DDMs) and their applications in solving electrically large and multi-scale electromagnetic (EM) radiation and scattering problems. In particular, a finite-element DDM, together with a finite-element tearing and interconnecting (FETI)-like algorithm, incorporating Robin transmission conditions and an edge corner penalty term , are discussed in detail. We address in full the formulations, and subsequently, their applications to problems with significant amounts of repetitions. The non-conformal DDM approach has also been extended into surface
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Zhou, Guo, Wang, et al. "Research on Fault Extraction Method of Variational Mode Decomposition Based on Immunized Fruit Fly Optimization Algorithm." Entropy 21, no. 4 (2019): 400. http://dx.doi.org/10.3390/e21040400.

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In recent years, a new method of fault diagnosis, named variational mode decomposition (VMD), has been widely used in industrial production, but the decomposition accuracy of VMD is determined by two parameters, which are respectively the decomposition layer number k and the penalty factor α, if the parameters are not properly selected, there will be over-decomposition or under-decomposition. In order to find an approach to determine the parameters adaptively, a method to optimize VMD by using the immune fruit fly optimization algorithm (IFOA) is proposed in this paper. In this method, permuta
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41

Göttlich, Simone, Falk M. Hante, Andreas Potschka, and Lars Schewe. "Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints." Mathematical Programming 188, no. 2 (2021): 599–619. http://dx.doi.org/10.1007/s10107-021-01656-9.

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AbstractWe consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without combinatorial constraints and a mixed-integer problem for the combinatorial constraints in the control space. Both problems can be solved very efficiently with existing methods such as outer convexification with sum-up-rounding strategies and mixed-integer linear programming techniques. The coupling is handled using a penalty-approach. We provide an exactn
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Rahman, Mustafizur, Debapriya Bhattacharya, and Md Al-Hasan. "Dimensions of Informality in Bangladesh Labour Market and the Consequent Wage Penalty." South Asia Economic Journal 20, no. 2 (2019): 224–47. http://dx.doi.org/10.1177/1391561419850303.

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The article examines the various dimensions and underlying causes of informal employment in the Bangladesh labour market and the associated wage penalty. Based on labour force survey data for successive points, we trace the dynamics of employment in Bangladesh along the informal–formal divide over time. Given that wage differential remains a key feature concerning the two market segments, we have carried out mean and quantile decomposition exercises to estimate the wage penalty originating from informality. We find significant wage gaps between formal- and informal-paid employees, formal paid
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Xie, Peng, Li Xu, Jun-Hui Yin, Hao Wang, Zhong-Hai Yang, and Bin Li. "An Interior Penalty Domain Decomposition Method for Thermal Analysis of 3-D Integrated Systems." IEEE Transactions on Components, Packaging and Manufacturing Technology 11, no. 3 (2021): 395–406. http://dx.doi.org/10.1109/tcpmt.2021.3054243.

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Shi, Qingjiang, and Mingyi Hong. "Penalty Dual Decomposition Method for Nonsmooth Nonconvex Optimization—Part I: Algorithms and Convergence Analysis." IEEE Transactions on Signal Processing 68 (2020): 4108–22. http://dx.doi.org/10.1109/tsp.2020.3001906.

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Laptin, Yu P. "Exact Penalty Functions and Convex Extensions of Functions in Schemes of Decomposition in Variables*." Cybernetics and Systems Analysis 52, no. 1 (2016): 85–95. http://dx.doi.org/10.1007/s10559-016-9803-8.

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46

Singh, Sahjendra N., James H. Myatt, Gregory A. Addington, Siva Banda, and James K. Hall. "Optimal Feedback Control of Vortex Shedding Using Proper Orthogonal Decomposition Models." Journal of Fluids Engineering 123, no. 3 (2001): 612–18. http://dx.doi.org/10.1115/1.1385513.

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This paper treats the question of control of two-dimensional incompressible, unsteady wake flow behind a circular cylinder at Reynolds number Re=100. Two finite-dimensional lower order models based on proper orthogonal decomposition (POD) are considered for the control system design. Control action is achieved via cylinder rotation. Linear optimal control theory is used for obtaining stabilizing feedback control systems. An expression for the region of stability of the system is derived. Simulation results for 18-mode POD models obtained using the control function and penalty methods are prese
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47

Madalozzo, Regina. "An analysis of income differentials by marital status." Estudos Econômicos (São Paulo) 38, no. 2 (2008): 267–92. http://dx.doi.org/10.1590/s0101-41612008000200003.

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Unmarried cohabitation has become a more frequently observed phenomenon over the last three decades, and not only in the United States. The objective of this work is to examine income differentials between married women and those who remain single or cohabitate. The empirical literature shows that, while the marriage premium is verified in different studies for men, the result for women is not conclusive. The main innovation of my study is the existence of controls for selection. In this study, we have two sources of selectivity: into the labor force and into a marital status category. The swi
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48

Jin, Zhihao, Guangdong Chen, and Zhengxin Yang. "Rolling Bearing Fault Diagnosis Based on WOA-VMD-MPE and MPSO-LSSVM." Entropy 24, no. 7 (2022): 927. http://dx.doi.org/10.3390/e24070927.

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In order to further improve the accuracy of fault identification of rolling bearings, a fault diagnosis method based on the modified particle swarm optimization (MPSO) algorithm optimized least square support vector machine (LSSVM), combining parameter optimization variational mode decomposition (VMD) and multi-scale permutation entropy (MPE), was proposed. Firstly, to solve the problem of insufficient decomposition and mode mixing caused by the improper selection of mode component K and penalty factor α in VMD algorithm, the whale optimization algorithm (WOA) was used to optimize the penalty
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Xuan, Menghui, Sixia Zhao, Mengnan Liu, Liyou Xu, and Xiaoliang Chen. "Inspection method of combine assembly quality based on optimized VMD." Journal of Physics: Conference Series 2125, no. 1 (2021): 012021. http://dx.doi.org/10.1088/1742-6596/2125/1/012021.

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Abstract Aiming at the problems of low assembly accuracy and difficult to detect assembly quality of combine, a method of combine assembly quality detection based on sparrow search algorithm (SSA) optimized variational mode decomposition (VMD) and particle swarm optimization (PSO) optimized least squares support vector machine (LSSVM) was proposed, Firstly, the sparrow search algorithm is used to obtain the optimal VMD decomposition modal parameter K and penalty factor α, then the combined vibration signal of combine harvester is decomposed into intrinsic modal components of different center f
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Li, Zhiyuan, Shun Li, Jiandong Mao, Juan Li, Qiang Wang, and Yi Zhang. "A Novel Lidar Signal-Denoising Algorithm Based on Sparrow Search Algorithm for Optimal Variational Modal Decomposition." Remote Sensing 14, no. 19 (2022): 4960. http://dx.doi.org/10.3390/rs14194960.

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Abstract:
Atmospheric lidar is susceptible to the influence of light attenuation, sky background light, and detector dark currents during the detection process. This results in a large amount of noise in the lidar return signal. To reduce noise and extract a useful signal, a novel denoising method combined with variational modal decomposition (VMD), the sparrow search algorithm (SSA) and singular value decomposition (SVD) is proposed. The SSA is used to optimize the number of decomposition layers K and the quadratic penalty factor α values of the VMD algorithm. Some intrinsic mode function (IMF) compone
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