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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year

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Sequential differentiation and its application to the theory of nonsmooth extremum problems

S. Ya. Serovaiskii

Al-Farabi Kazakh National University, al-Farabi ave., 71, Almaty, 480078, Kazakhstan. E-mail:

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 14, Issue 7, Pages 717–734, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939406779802013,

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Finding the derivative of a (discrepancy) functional under minimization is an important stage in the analysis of inverse and optimization problems. This problem becomes even more complicated if the state equation involves a nonsmooth operator. The encountered difficulties can be resolved by introducing the notion of sequential operator derivative, constructed by the principle of generalized-function derivative in the sequential distribution theory. In the latter case, the equation is approximated with a family of equations that involve smooth operators. A necessary extremum condition is derived which allows one to find an approximate solution to the problem. As an example, we consider a system governed by an elliptic-type equation with nonsmooth nonlinearity.

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