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A superlinearly convergent R-regularized Newton scheme for variational models with concave sparsity-promoting priors

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  • Michael Hintermüller
  • Tao Wu

Abstract

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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Michael Hintermüller & Tao Wu, 2014. "A superlinearly convergent R-regularized Newton scheme for variational models with concave sparsity-promoting priors," Computational Optimization and Applications, Springer, vol. 57(1), pages 1-25, January.
    • Handle: RePEc:spr:coopap:v:57:y:2014:i:1:p:1-25
    DOI: 10.1007/s10589-013-9583-2
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    References listed on IDEAS

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