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Title
A superlinearly convergent R-regularized Newton scheme for variational models with concave sparsity-promoting priors / M. Hintermueller, T. Wu
AuthorHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Wu, Tao
Published in
Computational Optimization and Applications, New York, NY [u.a.], 2014, Vol. 57, Issue 1, page 1-25
PublishedSpringer
LanguageEnglish
Document typeJournal Article
Keywords (EN)Sparsity / Concave priors / Nonconvex minimization / Semismooth Newton method / Superlinear convergence
ISSN1573-2894
URNurn:nbn:at:at-ubg:3-1947 Persistent Identifier (URN)
DOIdoi:10.1007/s10589-013-9583-2 
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 The work is publicly available
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A superlinearly convergent R-regularized Newton scheme for variational models with concave sparsity-promoting priors [3.83 mb]
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Abstract (English)

A general class of variational models with concave priors is considered for obtaining certain sparse solutions, for which nonsmoothness and non-Lipschitz continuity of the objective functions pose significant challenges from an analytical as well as numerical point of view. For computing a stationary point of the underlying variational problem, a Newton-type scheme with provable convergence properties is proposed. The possible non-positive definiteness of the generalized Hessian is handled by a tailored regularization technique, which is motivated by reweighting as well as the classical trust-region method. Our numerical experiments demonstrate selected applications in image processing, support vector machines, and optimal control of partial differential equations.

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