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

Sequential differentiation and its application to the theory of nonsmooth extremum problems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inverse and Ill-Posed Problems de Gruyter

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

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Publisher
de Gruyter
Copyright
Copyright 2006, Walter de Gruyter
ISSN
0928-0219
eISSN
1569-3953
DOI
10.1515/156939406779802013
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Journal of Inverse and Ill-Posed Problemsde Gruyter

Published: Dec 1, 2006

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