A unified framework for constructing globally convergent algorithms for multidimensional coefficient inverse problems

We present a unified framework for constructing the globally convergent algorithms for a broad class of multidimensional coefficient inverse problems arising in natural science and industry. Based on the convexification approach, the unified framework substantiates the numerical solution of the corr...

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Bibliographic Details
Published inApplicable analysis Vol. 83; no. 9; pp. 933 - 955
Main Authors Klibanov, Michael V., Timonov †, Alexandre
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.09.2004
Subjects
2000 Mathematics Subject Classifications: 35R20
Coefficient inverse problems
Computational experiments
Convexification approach
Globally convergent algoirthms
Multiextremality
Optical frequency sounding
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Summary:We present a unified framework for constructing the globally convergent algorithms for a broad class of multidimensional coefficient inverse problems arising in natural science and industry. Based on the convexification approach, the unified framework substantiates the numerical solution of the corresponding problem of nonconvex optimization. A globally convergent iterative algorithm for an inverse problem of diffuse optical mammography is constructed. It utilizes the contraction property of a nonlinear operator resulting from applying the convexification approach. The effectiveness of this algorithm is demonstrated in computational experiments.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036810410001712844