MADMM: a generic algorithm for non-smooth optimization on manifolds. Numerous problems in machine learning are formulated as optimization with manifold constraints. In this paper, we propose the Manifold alternating directions method of multipliers (MADMM), an extension of the classical ADMM scheme for manifold-constrained non-smooth optimization problems and show its application to several challenging problems in dimensionality reduction, data analysis, and manifold learning.

References in zbMATH (referenced in 14 articles )

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  1. Diepeveen, Willem; Lellmann, Jan: An inexact semismooth Newton method on Riemannian manifolds with application to duality-based total variation denoising (2021)
  2. Li, Xiao; Chen, Shixiang; Deng, Zengde; Qu, Qing; Zhu, Zhihui; Man-Cho So, Anthony: Weakly convex optimization over Stiefel manifold using Riemannian subgradient-type methods (2021)
  3. Sakakibara, Koya: Numerical analysis of constrained total variation flows (2021)
  4. Schonsheck, Stefan C.; Bronstein, Michael M.; Lai, Rongjie: Nonisometric surface registration via conformal Laplace-Beltrami basis pursuit (2021)
  5. Xiao, Nachuan; Liu, Xin; Yuan, Ya-xiang: Exact penalty function for (\ell_2,1) norm minimization over the Stiefel manifold (2021)
  6. Bergmann, Ronny; Herrmann, Marc; Herzog, Roland; Schmidt, Stephan; Vidal-Núñez, José: Total variation of the normal vector field as shape prior (2020)
  7. Chen, Shixiang; Ma, Shiqian; Man-Cho So, Anthony; Zhang, Tong: Proximal gradient method for nonsmooth optimization over the Stiefel manifold (2020)
  8. Giga, Yoshikazu; Sakakibara, Koya; Taguchi, Kazutoshi; Uesaka, Masaaki: A new numerical scheme for discrete constrained total variation flows and its convergence (2020)
  9. Hu, Jiang; Liu, Xin; Wen, Zai-Wen; Yuan, Ya-Xiang: A brief introduction to manifold optimization (2020)
  10. Liu, Changshuo; Boumal, Nicolas: Simple algorithms for optimization on Riemannian manifolds with constraints (2020)
  11. Zhang, Junyu; Ma, Shiqian; Zhang, Shuzhong: Primal-dual optimization algorithms over Riemannian manifolds: an iteration complexity analysis (2020)
  12. Zhou, Shenglong; Xiu, Naihua; Qi, Hou-Duo: Robust Euclidean embedding via EDM optimization (2020)
  13. Budninskiy, Max; Yin, Gloria; Feng, Leman; Tong, Yiying; Desbrun, Mathieu: Parallel transport unfolding: a connection-based manifold learning approach (2019)
  14. Zhu, Hong; Zhang, Xiaowei; Chu, Delin; Liao, Li-Zhi: Nonconvex and nonsmooth optimization with generalized orthogonality constraints: an approximate augmented Lagrangian method (2017)