In a Hilbert space we consider a class of conditionally well-posed inverse problems for which a Hölder-type estimate of conditional stability on a closed convex bounded subset holds. We investigate the Ivanov quasi-solution method and its finite-dimensional version associated with minimization of a multi-extremal discrepancy functional over a conditional stability set or over a finite-dimensional section of this set, respectively. For these optimization problems, we prove that each of their stationary points that is located not too far from the desired solution of the original inverse problem belongs to a small neighborhood of the solution. Estimates for the diameter of this neighborhood in terms of error levels in input data are also given.

中文翻译：

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与条件良好的逆问题相关的差异泛函平稳点的聚类效应

在希尔伯特空间中，我们考虑一类条件良好的逆问题，对于该问题，Hölder型估计在封闭凸有界子集中的条件稳定性成立。我们分别研究了Ivanov拟解方法及其与在条件稳定性集或该集的有限维截面上使多个极值差异函数最小化相关的有限维版本。对于这些优化问题，我们证明了它们的每个固定点与原始逆问题的期望解相距不太远，都属于该解的一小部分。还给出了根据输入数据中的误差水平对该邻域的直径的估计。