Regularization tools and robust optimization for ill‐conditioned least squares problem: A computational comparison

Regularization tools and robust optimization for ill‐conditioned least squares problem: A computational comparison

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Article ID: iaor20115457
Volume: 217
Issue: 20
Start Page Number: 7985
End Page Number: 7990
Publication Date: Jun 2011
Journal: Applied Mathematics and Computation
Authors:
Keywords: regularisation techniques, robust optimization, least squares
Abstract:

Least squares problems arise frequently in many disciplines such as image restorations. In these areas, for the given least squares problem, usually the coefficient matrix is ill‐conditioned. Thus if the problem data are available with certain error, then after solving least squares problem with classical approaches we might end up with a meaningless solution. Tikhonov regularization, is one of the most widely used approaches to deal with such situations. In this paper, first we briefly describe these approaches, then the robust optimization framework which includes the errors in problem data is presented. Finally, our computational experiments on several ill‐conditioned standard test problems using the regularization tools, a Matlab package for least squares problem, and the robust optimization framework, show that the latter approach may be the right choice.

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