FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2015300527> ?p ?o ?g. }

• W2015300527 endingPage "123001" @default.
• W2015300527 startingPage "123001" @default.
• W2015300527 abstract "The investigation of regularization schemes with sparsity promoting penalty terms has been one of the dominant topics in the field of inverse problems over the last years, and Tikhonov functionals with lp-penalty terms for 1 ⩽ p ⩽ 2 have been studied extensively. The first investigations focused on regularization properties of the minimizers of such functionals with linear operators and on iteration schemes for approximating the minimizers. These results were quickly transferred to nonlinear operator equations, including nonsmooth operators and more general function space settings. The latest results on regularization properties additionally assume a sparse representation of the true solution as well as generalized source conditions, which yield some surprising and optimal convergence rates. The regularization theory with lp sparsity constraints is relatively complete in this setting; see the first part of this review. In contrast, the development of efficient numerical schemes for approximating minimizers of Tikhonov functionals with sparsity constraints for nonlinear operators is still ongoing. The basic iterated soft shrinkage approach has been extended in several directions and semi-smooth Newton methods are becoming applicable in this field. In particular, the extension to more general non-convex, non-differentiable functionals by variational principles leads to a variety of generalized iteration schemes. We focus on such iteration schemes in the second part of this review. A major part of this survey is devoted to applying sparsity constrained regularization techniques to parameter identification problems for partial differential equations, which we regard as the prototypical setting for nonlinear inverse problems. Parameter identification problems exhibit different levels of complexity and we aim at characterizing a hierarchy of such problems. The operator defining these inverse problems is the parameter-to-state mapping. We first summarize some general analytic properties derived from the weak formulation of the underlying differential equation, and then analyze several concrete parameter identification problems in detail. Naturally, it is not possible to cover all interesting parameter identification problems. In particular we do not include problems related to inverse scattering or nonlinear tomographic problems such as optical, thermo-acoustic or opto-acoustic imaging. Also we do not review the extensive literature on the closely related field of control problems for partial differential equations. However, we include one example which highlights the differences and similarities between control theory and the inverse problems approach in this context." @default.
• W2015300527 created "2016-06-24" @default.
• W2015300527 creator A5014074603 @default.
• W2015300527 creator A5039605463 @default.
• W2015300527 date "2012-11-26" @default.
• W2015300527 modified "2023-09-25" @default.
• W2015300527 title "Sparsity regularization for parameter identification problems" @default.
• W2015300527 cites W1531455566 @default.
• W2015300527 cites W1545334034 @default.
• W2015300527 cites W1559113676 @default.
• W2015300527 cites W1561641547 @default.
• W2015300527 cites W1570089119 @default.
• W2015300527 cites W1578285471 @default.
• W2015300527 cites W1579781026 @default.
• W2015300527 cites W1963605855 @default.
• W2015300527 cites W1965004103 @default.
• W2015300527 cites W1966384044 @default.
• W2015300527 cites W1971508657 @default.
• W2015300527 cites W1975490585 @default.
• W2015300527 cites W1987022245 @default.
• W2015300527 cites W1988920101 @default.
• W2015300527 cites W1993118533 @default.
• W2015300527 cites W1993692881 @default.
• W2015300527 cites W1994097344 @default.
• W2015300527 cites W1994569450 @default.
• W2015300527 cites W2004716871 @default.
• W2015300527 cites W2005089986 @default.
• W2015300527 cites W2005681075 @default.
• W2015300527 cites W2005782434 @default.
• W2015300527 cites W2005890786 @default.
• W2015300527 cites W2006262045 @default.
• W2015300527 cites W2008971399 @default.
• W2015300527 cites W2010586622 @default.
• W2015300527 cites W2013830829 @default.
• W2015300527 cites W2017848200 @default.
• W2015300527 cites W2018816711 @default.
• W2015300527 cites W2021182952 @default.
• W2015300527 cites W2022816471 @default.
• W2015300527 cites W2022920697 @default.
• W2015300527 cites W2023206259 @default.
• W2015300527 cites W2023299560 @default.
• W2015300527 cites W2024662962 @default.
• W2015300527 cites W2025495149 @default.
• W2015300527 cites W2027547498 @default.
• W2015300527 cites W2028452438 @default.
• W2015300527 cites W2029251197 @default.
• W2015300527 cites W2031604650 @default.
• W2015300527 cites W2033106066 @default.
• W2015300527 cites W2033515444 @default.
• W2015300527 cites W2034612641 @default.
• W2015300527 cites W2036854321 @default.
• W2015300527 cites W2037396431 @default.
• W2015300527 cites W2044461626 @default.
• W2015300527 cites W2046005774 @default.
• W2015300527 cites W2051561721 @default.
• W2015300527 cites W2052625285 @default.
• W2015300527 cites W2053405325 @default.
• W2015300527 cites W2053831664 @default.
• W2015300527 cites W2060041011 @default.
• W2015300527 cites W2063781300 @default.
• W2015300527 cites W2068039185 @default.
• W2015300527 cites W2070815098 @default.
• W2015300527 cites W2075324846 @default.
• W2015300527 cites W2077204104 @default.
• W2015300527 cites W2082823585 @default.
• W2015300527 cites W2082949320 @default.
• W2015300527 cites W2085102456 @default.
• W2015300527 cites W2098003450 @default.
• W2015300527 cites W2100414529 @default.
• W2015300527 cites W2105944420 @default.
• W2015300527 cites W2112890043 @default.
• W2015300527 cites W2114456237 @default.
• W2015300527 cites W2115706991 @default.
• W2015300527 cites W2117607492 @default.
• W2015300527 cites W2124257562 @default.
• W2015300527 cites W2124595012 @default.
• W2015300527 cites W2124929650 @default.
• W2015300527 cites W2126607811 @default.
• W2015300527 cites W2128648870 @default.
• W2015300527 cites W2138838870 @default.
• W2015300527 cites W2139665062 @default.
• W2015300527 cites W2140446903 @default.
• W2015300527 cites W2143163067 @default.
• W2015300527 cites W2147253850 @default.
• W2015300527 cites W2154615478 @default.
• W2015300527 cites W2156062145 @default.
• W2015300527 cites W2167400582 @default.
• W2015300527 cites W2170164530 @default.
• W2015300527 cites W2278331350 @default.
• W2015300527 cites W2314826591 @default.
• W2015300527 cites W2325820873 @default.
• W2015300527 cites W2488131745 @default.
• W2015300527 cites W2601777109 @default.
• W2015300527 cites W2742470390 @default.
• W2015300527 cites W2950042078 @default.
• W2015300527 cites W2963756161 @default.
• W2015300527 cites W3098608218 @default.
• W2015300527 cites W3101710822 @default.

• next