MADMM swMATH ID: 38277 Software Authors: Artiom Kovnatsky, Klaus Glashoff, Michael M. Bronstein Description: 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. Homepage: https://arxiv.org/abs/1505.07676 Related Software: Manopt; SDPLR; Matrix Means Toolbox; FPC_AS; FMS; GradSamp; AdaGrad; BiqMac; Biq Mac; PDCO; CVX; Spectra; Europarl; PMA; Steerable pyramid; Manopt.jl; Camino; RecPF; UCI-ml; ROPTLIB Cited in: 16 Publications all top 5 Cited by 53 Authors 2 Chen, Shixiang 2 Liu, Xin 2 Ma, Shiqian 2 Sakakibara, Koya 2 So, Anthony Man-Cho 2 Yuan, Ya-xiang 1 Bergmann, Ronny 1 Boumal, Nicolas 1 Bronstein, Michael M. 1 Budninskiy, Max 1 Chu, Delin 1 Deng, Zengde 1 Desbrun, Mathieu 1 Diepeveen, Willem 1 Feng, Leman 1 Giga, Yoshikazu 1 Herrmann, Marc 1 Herzog, Roland 1 Hu, Jiang 1 Lai, Rongjie 1 Lellmann, Jan 1 Li, Guoqi 1 Li, Xiao 1 Liao, Li-Zhi 1 Liu, Changshuo 1 Maass, Alejandro I. 1 Manton, Jonathan H. 1 Manzie, Chris 1 Meng, Ziyang 1 Nešić, Dragan 1 Pei, Jing 1 Qi, Houduo 1 Qu, Qing 1 Schmidt, Stephan 1 Schonsheck, Stefan C. 1 Shames, Iman 1 Shi, Luping 1 Taguchi, Kazutoshi 1 Tang, Pei 1 Tong, Yiying 1 Uesaka, Masaaki 1 Vidal-Nuñez, José 1 Wen, Changyun 1 Wen, Zaiwen 1 Xiao, Nachuan 1 Xiu, Naihua 1 Yin, Gloria 1 Zhang, Junyu 1 Zhang, Shuzhong 1 Zhang, Xiaowei 1 Zhou, Shenglong 1 Zhu, Hong 1 Zhu, Zhihui all top 5 Cited in 11 Serials 4 SIAM Journal on Optimization 2 Journal of Scientific Computing 1 Inverse Problems 1 Physica A 1 Applied Mathematics and Optimization 1 Numerische Mathematik 1 Mathematical Programming. Series A. Series B 1 SIAM Journal on Imaging Sciences 1 Mathematical Programming Computation 1 Journal of the Operations Research Society of China 1 SIAM Journal on Applied Algebra and Geometry all top 5 Cited in 8 Fields 11 Operations research, mathematical programming (90-XX) 10 Numerical analysis (65-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Computer science (68-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Partial differential equations (35-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year