Abstract This paper presents a multi-objective optimization approach for choosing an appropriate regularization parameter in Tikhonov-type regularization of discrete ill-posed problems. Finding the regularization parameter is formulated as a multi-objective optimization problem and some transformations are introduced to construct a new problem equivalent to it. Then, by using the standard multi-objective optimization methods, a single-objective problem is derived that its minimizer gives a proper estimation of the regularization parameter. Via considering some test problems, the numerical efficiency of the presented method is compared with the L-curve and the GCV parameter choice methods.

中文翻译：

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通过求解多目标优化问题确定正则化参数

摘要 本文提出了一种多目标优化方法，用于在离散不适定问题的 Tikhonov 型正则化中选择合适的正则化参数。寻找正则化参数被表述为一个多目标优化问题，并引入了一些变换来构造一个等效的新问题。然后，通过使用标准的多目标优化方法，推导出一个单目标问题，其最小值给出了正则化参数的正确估计。通过考虑一些测试问题，将所提出方法的数值效率与L曲线和GCV参数选择方法进行了比较。