This article is cited in 1 scientific paper (total in 1 paper)
Convergence rate estimates for Tikhonov's scheme as applied to ill-posed nonconvex optimization problems
M. Yu. Kokurin
Mari State University, Yoshkar-Ola, Russia
We examine the convergence rate of approximations generated by Tikhonov's scheme as applied to ill-posed constrained optimization problems with general smooth functionals on a convex closed subset of a Hilbert space. Assuming that the solution satisfies a source condition involving the second derivative of the cost functional and depending on the form of constraints, we establish the convergence rate of the Tikhonov approximations in the cases of exact and approximately specified functionals.
ill-posed optimization problem in a Hilbert space, convex closed set, Tikhonov's scheme, convergence rate, source condition.
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Computational Mathematics and Mathematical Physics, 2017, 57:7, 1101–1110
M. Yu. Kokurin, “Convergence rate estimates for Tikhonov's scheme as applied to ill-posed nonconvex optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 57:7 (2017), 1103–1112; Comput. Math. Math. Phys., 57:7 (2017), 1101–1110
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\paper Convergence rate estimates for Tikhonov's scheme as applied to ill-posed nonconvex optimization problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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M. Yu. Kokurin, “Solution of ill-posed nonconvex optimization problems with accuracy proportional to the error in input data”, Comput. Math. Math. Phys., 58:11 (2018), 1748–1760
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