Levenberg–Marquardt method in Banach spaces with general convex regularization terms

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• 作者：Qinian Jin ; Hongqi Yang
• 刊名：Numerische Mathematik
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：133
• 期：4
• 页码：655-684
• 全文大小：997 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Numerical Analysis
  Mathematics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  Numerical and Computational Methods
  Applied Mathematics and Computational Methods of Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：0945-3245
• 卷排序：133

文摘

We propose a Levenberg–Marquardt method with general uniformly convex regularization terms to solve nonlinear inverse problems in Banach spaces, which is an extension of the scheme proposed by Hanke in (Inverse Probl 13:79–95, 1997) in Hilbert space setting. The method is so designed that it can be used to detect the features of the sought solutions such as sparsity or piecewise constancy. It can also be used to deal with the situation that the data is contaminated by noise containing outliers. By using tools from convex analysis in Banach spaces, we establish the convergence of the method. Numerical simulations are reported to test the performance of the method.Mathematics Subject Classification65J1565J2047H17