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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Bibliographic Details
Published in:Mathematical problems in engineering Vol. 2019; no. 2019; pp. 1 - 8
Main Authors: Fu, Zhengqing, Guo, Lanlan, Liu, Guolin
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Publishing Corporation 2019
Hindawi
John Wiley & Sons, Inc
Subjects:
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
ISSN:1024-123X, 1563-5147
Online Access:Get full text
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Summary: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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ISSN:1024-123X
1563-5147
DOI:10.1155/2019/3087949