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Computational Mathematics and Mathematical Physics

, Volume 58, Issue 11, pp 1748–1760 | Cite as

Solution of Ill-Posed Nonconvex Optimization Problems with Accuracy Proportional to the Error in Input Data

  • M. Yu. Kokurin
Article
  • 7 Downloads

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.

Keywords:

ill-posed optimization problem error Hilbert space convex closed set Minkowski functional Tikhonov’s scheme gradient projection method accuracy estimate 

Notes

ACKNOWLEDGMENTS

This work was supported by the Russian Foundation for Basic Research, project no. 16-01-00039a.

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Mari State UniversityYoshkar-OlaRussia

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