Secant variable projection method for solving nonnegative separable least squares problems
Secant variable projection method for solving nonnegative separable least squares problems
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DOI：
10.1007/s11075-019-00835-2
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发表时间：
2020-03
影响因子：
2.1
通讯作者：
Xiongfeng Song;W. Xu;K. Hayami;Ning Zheng
中科院分区：
文献类型：
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作者：
Xiongfeng Song;W. Xu;K. Hayami;Ning Zheng
变量投影法是求解可分离非线性最小二乘问题的一种经典而有效的方法。然而，它是很难处理的约束SNLLS问题，因为雅可比矩阵的显式形式需要在每次迭代。在本文中，我们提出了一个割线变量投影（SVP）方法，它采用秩一更新估计雅可比矩阵。我们的方法的主要优点是效率和易于适用于约束SNLLS问题。我们的SVP方法的局部收敛性进行了分析。最后，解决了一些数据拟合和图像处理问题，比较我们提出的方法与经典的可变投影方法的性能。数值结果表明，我们提出的SVP方法在解决盲反卷积问题中产生的SNLLS问题时是有效的和稳定的。
The variable projection method is a classical and efficient method for solving separable nonlinear least squares (SNLLS) problems. However, it is hard to handle the constrained SNLLS problems since the explicit form of the Jacobian matrix is required in each iteration. In this paper, we propose a secant variable projection (SVP) method, which employs a rank-one update to estimate the Jacobian matrices. The main advantages of our method are efficiency and ease of applicability to constrained SNLLS problems. The local convergence of our SVP method is also analyzed. Finally, some data fitting and image processing problems are solved to compare the performance of our proposed method with the classical variable projection method. Numerical results illustrate the efficiency and stability of our proposed SVP method in solving the SNLLS problems arising from the blind deconvolution problems.