This article is cited in 2 papers

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.

UDC: 517.988

Received: 30.01.2017

DOI: 10.31857/S004446690003535-9

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

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