This article is cited in 19 papers

On the convexity of the Tikhonov functional and iteratively regularized methods for solving irregular nonlinear operator equations

M. Yu. Kokurin

Mari State University, pl. Lenina 1, Yoshkar-Ola, 424001 Russia

Abstract: Domains in a Hilbert space are localized where the Tikhonov functional of an irregular nonlinear operator equation is either strongly convex or has other similar properties. Depending on the sourcewise representability conditions imposed on the solution, four such domains are detected, and their size is estimated. These results are used to substantiate the general scheme for the design of nonlocal two-level iterative processes for solving irregular equations.

Key words: ill-posed problem, Tikhonov scheme, global optimization, strong convexity, Fejér mapping, sourcewise representability, numerical solution of operator equation.

UDC: 519.642.8

Received: 15.09.2009

 English version: Computational Mathematics and Mathematical Physics, 2010, 50:4, 620–632

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