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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| Published in | Applicable analysis Vol. 83; no. 9; pp. 933 - 955 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.09.2004
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0003-6811 1563-504X |
| DOI | 10.1080/00036810410001712844 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Timonov †, Alexandre Klibanov, Michael V. |
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| CitedBy_id | crossref_primary_10_1080_00036811_2010_483431 crossref_primary_10_1109_MCSE_2010_22 crossref_primary_10_1002_cnm_971 crossref_primary_10_1016_j_jtbi_2006_11_013 crossref_primary_10_1137_070691206 crossref_primary_10_1016_j_apnum_2004_09_031 crossref_primary_10_1515_JIIP_2007_009 crossref_primary_10_1080_00036810701609869 crossref_primary_10_1080_17415970802015856 crossref_primary_10_1088_1742_6596_290_1_012015 crossref_primary_10_1088_0266_5611_26_11_115007 crossref_primary_10_1515_JIIP_2009_016 |
| Cites_doi | 10.1088/0031-9155/40/1/001 10.1098/rstb.1997.0047 10.1088/0266-5611/19/2/312 10.1093/clinchem/38.9.1618 10.1088/0266-5611/7/6/011 10.1088/0266-5611/19/2/306 10.1007/978-1-4899-0030-2 10.1088/0266-5611/13/3/008 10.1088/0266-5611/17/6/320 10.1088/0266-5611/18/2/306 |
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| References | G VG (bib16) 1987 M MM (bib15) 1972 A CA (bib11) 1996 M PM (bib18) 1953 bib14 bib12 bib13 Klibanov MV (bib5) 2001; 17 M MM (bib1) 1986 Tromberg (bib10) 1995; 40 bib20 Ishimaru A (bib19) 1978 H JH (bib17) 1967 Fletcher R (bib4) 1987 bib6 Tikhonov AN (bib2) 1998 Isakov V (bib3) 1998 Klibanov MV (bib7) 2003; 4 Robinson M (bib8) 1992; 38 J BJ (bib9) 1997; 352 |
| References_xml | – volume: 40 start-page: 1 year: 1995 ident: bib10 publication-title: Phys. Med. Biol. doi: 10.1088/0031-9155/40/1/001 – volume: 352 start-page: 661 year: 1997 ident: bib9 publication-title: Phil. Trans. R. Soc. Lond. B doi: 10.1098/rstb.1997.0047 – ident: bib14 doi: 10.1088/0266-5611/19/2/312 – volume: 38 start-page: 1618 year: 1992 ident: bib8 publication-title: Clinical Chemistry doi: 10.1093/clinchem/38.9.1618 – volume-title: Ill-Posed Problems of Mathematical Physics and Analysis, AMS year: 1986 ident: bib1 – ident: bib12 doi: 10.1088/0266-5611/7/6/011 – ident: bib6 doi: 10.1088/0266-5611/19/2/306 – volume-title: State of the Art in Global Optimization, Kluwer year: 1996 ident: bib11 – volume-title: Inverse Problems for Partial Differential Equations, Springer year: 1998 ident: bib3 doi: 10.1007/978-1-4899-0030-2 – ident: bib20 doi: 10.1088/0266-5611/13/3/008 – volume-title: Practical Methods of Optimization year: 1987 ident: bib4 – volume-title: Inverse Problems of Mathematical Physics, VNU year: 1987 ident: bib16 – volume-title: Nonlinear Ill-Posed Problems, Chapman and Hall year: 1998 ident: bib2 – volume-title: Methods of Theoretical Physics, McGraw-Hill year: 1953 ident: bib18 – volume-title: The Theory of Splines and Their Applications, Academic Press year: 1967 ident: bib17 – volume-title: The Variational Method and The Method of Monotone Operators year: 1972 ident: bib15 – volume: 17 start-page: 1865 year: 2001 ident: bib5 publication-title: Inverse Problems doi: 10.1088/0266-5611/17/6/320 – volume: 4 start-page: 52 year: 2003 ident: bib7 publication-title: Numerical Methods and Programming – ident: bib13 doi: 10.1088/0266-5611/18/2/306 – volume-title: Wave Propagation and Scattering in Random Media. Vol. I: Single Scattering and Transport Theory, Academic Press year: 1978 ident: bib19 |
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| SubjectTerms | 2000 Mathematics Subject Classifications: 35R20 Coefficient inverse problems Computational experiments Convexification approach Globally convergent algoirthms Multiextremality Optical frequency sounding |
| Title | A unified framework for constructing globally convergent algorithms for multidimensional coefficient inverse problems |
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