Sequential Quadratic Programming Method for Nonlinear Least Squares Estimation and Its Application
In this study, we propose a direction-controlled nonlinear least squares estimation model that combines the penalty function and sequential quadratic programming. The least squares model is transformed into a sequential quadratic programming model, allowing for the iteration direction to be controll...
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| Vydané v: | Mathematical problems in engineering Ročník 2019; číslo 2019; s. 1 - 8 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Cairo, Egypt
Hindawi Publishing Corporation
2019
Hindawi John Wiley & Sons, Inc |
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| ISSN: | 1024-123X, 1563-5147 |
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| Abstract | In this study, we propose a direction-controlled nonlinear least squares estimation model that combines the penalty function and sequential quadratic programming. The least squares model is transformed into a sequential quadratic programming model, allowing for the iteration direction to be controlled. An ill-conditioned matrix is processed by our model; the least squares estimate, the ridge estimate, and the results are compared based on a combination of qualitative and quantitative analyses. For comparison, we use two equality indicators: estimated residual fluctuation of different methods and the deviation between estimated and true values. The root-mean-squared error and standard deviation are used for quantitative analysis. The results demonstrate that our proposed model has a smaller error than other methods. Our proposed model is thereby found to be effective and has high precision. It can obtain more precise results compared with other classical unwrapping algorithms, as shown by unwrapping using both simulated and real data from the Jining area in China. |
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| AbstractList | In this study, we propose a direction-controlled nonlinear least squares estimation model that combines the penalty function and sequential quadratic programming. The least squares model is transformed into a sequential quadratic programming model, allowing for the iteration direction to be controlled. An ill-conditioned matrix is processed by our model; the least squares estimate, the ridge estimate, and the results are compared based on a combination of qualitative and quantitative analyses. For comparison, we use two equality indicators: estimated residual fluctuation of different methods and the deviation between estimated and true values. The root-mean-squared error and standard deviation are used for quantitative analysis. The results demonstrate that our proposed model has a smaller error than other methods. Our proposed model is thereby found to be effective and has high precision. It can obtain more precise results compared with other classical unwrapping algorithms, as shown by unwrapping using both simulated and real data from the Jining area in China. |
| Author | Guo, Lanlan Fu, Zhengqing Liu, Guolin |
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| Cites_doi | 10.1016/j.amc.2006.08.034 10.1016/j.nonrwa.2005.06.003 10.22436/jnsa.009.06.84 10.1016/j.nonrwa.2015.05.005 10.1007/s10589-015-9744-6 10.12785/amis/080465 10.1016/j.jspi.2014.11.001 10.1155/2013/295147 10.1016/j.amc.2012.11.020 10.1007/s10255-013-0218-2 10.12785/amis/070637 10.1007/s11424-017-5308-4 10.1515/jnum-2013-0012 10.1016/j.cam.2014.12.021 10.1016/j.amc.2018.01.049 10.1007/s11590-015-0863-x 10.1007/s11228-013-0260-5 10.1080/02331934.2012.678849 10.1016/j.amc.2014.10.075 10.1007/s11590-011-0432-x 10.1007/s40314-013-0012-z 10.1016/j.amc.2013.12.169 10.1007/s10255-013-0300-9 10.1155/2014/470320 10.1155/2013/545147 10.22436/jnsa.010.08.07 10.1080/01630563.2013.814667 10.1007/s10255-017-0697-7 10.1007/s40314-014-0137-8 10.1007/s11336-013-9377-6 |
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| Copyright | Copyright © 2019 Zhengqing Fu et al. Copyright © 2019 Zhengqing Fu et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| SubjectTerms | Algorithms Applied mathematics Computer simulation Conditioning Economic models Iterative methods Least squares Mathematical programming Nonlinear control Penalty function Quadratic programming Qualitative analysis Quantitative analysis Queuing theory Variations |
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| Title | Sequential Quadratic Programming Method for Nonlinear Least Squares Estimation and Its Application |
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