A semismooth Newton method with analytical path-following for the $H^1$-projection onto the Gibbs simplex. (7th June 2018)

• Record Type: Journal Article
• Authors: Adam, L; Hintermüller, M; Surowiec, T M
• Is Part Of: IMA journal of numerical analysis. Volume 39:Number 3(2019)
• Page Start: 1276
• Page End: 1295
• Publication Date: 2018-06-07
• Subjects: Gibbs simplex -- metric projection -- semismooth Newton -- path-following -- Ginzburg–Landau energy -- multiphase field models -- inpainting -- data classification; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry034
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: An efficient, function-space-based second-order method for the $H^1$ -projection onto the Gibbs simplex is presented. The method makes use of the theory of semismooth Newton methods in function spaces as well as Moreau–Yosida regularization and techniques from parametric optimization. A path-following technique is considered for the regularization parameter updates. A rigorous first- and second-order sensitivity analysis of the value function for the regularized problem is provided to justify the update scheme. The viability of the algorithm is then demonstrated for two applications found in the literature: binary image inpainting and labeled data classification. In both cases, the algorithm exhibits mesh-independent behavior.