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

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 tha...

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Veröffentlicht in:Computational mathematics and mathematical physics Jg. 58; H. 11; S. 1748 - 1760
1. Verfasser: Kokurin, M. Yu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Moscow Pleiades Publishing 01.11.2018
Springer Nature B.V
Schlagworte:
Accuracy
Computational Mathematics and Numerical Analysis
Hilbert space
Ill posed problems
Mathematics
Mathematics and Statistics
Nonlinear programming
Optimization
Smooth boundaries
ill-posed optimization problem
Tikhonov’s scheme
accuracy estimate
Minkowski functional
gradient projection method
convex closed set
Hilbert space
error
ISSN:0965-5425, 1555-6662
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542518110064