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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 11, Pages 1815–1828 (Mi zvmmf10854)  

Solution of ill-posed nonconvex optimization problems with accuracy proportional to the error in input data

M. Yu. Kokurin

Mari State University, Yoshkar-Ola, Russia

Abstract: The ill-posed problem of minimizing an approximately specified smooth nonconvex functional on a convex closed subset of a Hilbert space is considered. For the class of problems characterized by a feasible set with a nonempty interior and a smooth boundary, regularizing procedures are constructed that ensure an accuracy estimate proportional or close to the error in the input data. The procedures are generated by the classical Tikhonov scheme and a gradient projection technique. A necessary condition for the existence of procedures regularizing the class of optimization problems with a uniform accuracy estimate in the class is established.

Key words: ill-posed optimization problem, error, Hilbert space, convex closed set, Minkowski functional, Tikhonov's scheme, gradient projection method, accuracy estimate.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00039_a


DOI: https://doi.org/10.31857/S004446690003535-9

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:11, 1748–1760

Bibliographic databases:

UDC: 517.988
Received: 30.01.2017

Citation: M. Yu. Kokurin, “Solution of ill-posed nonconvex optimization problems with accuracy proportional to the error in input data”, Zh. Vychisl. Mat. Mat. Fiz., 58:11 (2018), 1815–1828; Comput. Math. Math. Phys., 58:11 (2018), 1748–1760

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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