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 title: Variational Inequalities and Morozov\'s Discrepancy Principle name: Anzengruber first name: Stephan location/conference: cssip10 PRESENTATION-link: http://www.dfg-spp1324.de/nuhagtools/event/dateien/talks_cssip/anzengruber.pdf abstract: Variational Inequalities can be viewed as generalizations of classical source conditions and structural assumptions. In this talk we will show how, for non-linear ill-posed problems, Variational Inequalities can be combined with Morozov\'s Discrepancy principle to obtain convergence rates for Tikhonov Regularization with $\ell_p$ penalties, $p \geq 1$, which are well-known to promote sparsity.