The clustering effect for stationary points of discrepancy functionals associated with conditionally well-posed inverse problems
M.Yu. Kokurin
Mary State University, Lenin sqr., 1, Yoshkar-Ola, 424000
Keywords: обратная задача, условно-корректная задача, метод квазирешений, глобальная оптимизация, конечномерное подпространство, оценка точности, эффект кластеризации, inverse problem, conditionally well-posed problem, quasisolution method, global optimization, finite dimensional subspace, accuracy estimate, clustering effect
Abstract
In the Hilbert space, we consider a class of conditionally well-posed inverse problems, for which the Hölder type estimate of conditional stability on a closed convex bounded subset holds. We investigate the Ivanov quasisolution method and its finite dimensional version associated with the minimizing a multi-extremal discrepancy functional over a conditional stability set and over the finite dimensional section of this set, respectively. For these optimization problems, we prove that each their stationary point that is located not too far from the desired solution of the original inverse problem, in reality 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.
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