{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T21:31:07Z","timestamp":1781904667332,"version":"3.54.5"},"publisher-location":"Cham","reference-count":53,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319464534","type":"print"},{"value":"9783319464541","type":"electronic"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-46454-1_41","type":"book-chapter","created":{"date-parts":[[2016,9,15]],"date-time":"2016-09-15T09:15:09Z","timestamp":1473930909000},"page":"680-696","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":71,"title":["MADMM: A Generic Algorithm for Non-smooth Optimization on Manifolds"],"prefix":"10.1007","author":[{"given":"Artiom","family":"Kovnatsky","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Klaus","family":"Glashoff","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael M.","family":"Bronstein","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,9,16]]},"reference":[{"issue":"4","key":"41_CR1","doi-asserted-by":"publisher","first-page":"905","DOI":"10.1109\/TSP.2013.2295553","volume":"62","author":"X Dong","year":"2014","unstructured":"Dong, X., Frossard, P., Vandergheynst, P., Nefedov, N.: Clustering on multi-layer graphs via subspace analysis on Grassmann manifolds. Trans. Sig. Process. 62(4), 905\u2013918 (2014)","journal-title":"Trans. Sig. Process."},{"key":"41_CR2","unstructured":"Keshavan, R.H., Oh, S.: A gradient descent algorithm on the Grassman manifold for matrix completion (2009). arXiv:0910.5260"},{"key":"41_CR3","doi-asserted-by":"crossref","unstructured":"Boufounos, P.T., Baraniuk, R.G.: 1-bit compressive sensing. In: Proceedings of CISS (2008)","DOI":"10.1109\/CISS.2008.4558487"},{"issue":"2","key":"41_CR4","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1111\/cgf.12064","volume":"32","author":"A Kovnatsky","year":"2013","unstructured":"Kovnatsky, A., Bronstein, M.M., Bronstein, A.M., Glashoff, K., Kimmel, R.: Coupled quasi-harmonic bases. Comput. Graph. Forum 32(2), 439\u2013448 (2013)","journal-title":"Comput. Graph. Forum"},{"issue":"12","key":"41_CR5","doi-asserted-by":"publisher","first-page":"2505","DOI":"10.1109\/TPAMI.2015.2408348","volume":"37","author":"D Eynard","year":"2015","unstructured":"Eynard, D., Kovnatsky, A., Bronstein, M.M., Glashoff, K., Bronstein, A.M.: Multimodal manifold analysis using simultaneous diagonalization of Laplacians. Trans. PAMI 37(12), 2505\u20132517 (2015)","journal-title":"Trans. PAMI"},{"issue":"3","key":"41_CR6","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1145\/2240092.2240093","volume":"8","author":"M Cucuringu","year":"2012","unstructured":"Cucuringu, M., Lipman, Y., Singer, A.: Sensor network localization by eigenvector synchronization over the Euclidean group. ACM Trans. Sensor Netw. 8(3), 19 (2012)","journal-title":"ACM Trans. Sensor Netw."},{"issue":"1","key":"41_CR7","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1093\/imaiai\/ias002","volume":"1","author":"M Cucuringu","year":"2012","unstructured":"Cucuringu, M., Singer, A., Cowburn, D.: Eigenvector synchronization, graph rigidity and the molecule problem. Inf. Inference 1(1), 21\u201367 (2012)","journal-title":"Inf. Inference"},{"key":"41_CR8","doi-asserted-by":"crossref","unstructured":"Arie-Nachimson, M., Kovalsky, S.Z., Kemelmacher-Shlizerman, I., Singer, A., Basri, R.: Global motion estimation from point matches. In: Proceedings of 3DIMPVT (2012)","DOI":"10.1109\/3DIMPVT.2012.46"},{"key":"41_CR9","unstructured":"Zhang, M., Fletcher, P.T.: Probabilistic principal geodesic analysis. In: Proceedings of NIPS (2013)"},{"issue":"5","key":"41_CR10","doi-asserted-by":"publisher","first-page":"2327","DOI":"10.1137\/080731359","volume":"20","author":"M Journ\u00e9e","year":"2010","unstructured":"Journ\u00e9e, M., Bach, F., Absil, P.A., Sepulchre, R.: Low-rank optimization on the cone of positive semidefinite matrices. SIAM J. Optimization 20(5), 2327\u20132351 (2010)","journal-title":"SIAM J. Optimization"},{"key":"41_CR11","unstructured":"Meyer, G., Bonnabel, S., Sepulchre, R.: Linear regression under fixed-rank constraints: a Riemannian approach. In: Proceedings of ICML (2011)"},{"key":"41_CR12","unstructured":"Boumal, N., Absil, P.A.: RTRMC: A Riemannian trust-region method for low-rank matrix completion. In: Procedings of NIPS, pp. 406\u2013414 (2011)"},{"key":"41_CR13","unstructured":"Tan, M., Tsang, I.W., Wang, L., Vandereycken, B., Pan, S.J.: Riemannian pursuit for big matrix recovery. In: Proceedings of ICML (2014)"},{"key":"41_CR14","unstructured":"Shalit, U., Weinshall, D., Chechik, G.: Online learning in the manifold of low-rank matrices. In: Proceedings of NIPS (2010)"},{"key":"41_CR15","unstructured":"Absil, P.A., Gallivan, K.A.: Joint diagonalization on the oblique manifold for independent component analysis. In: Proceedings of ICASSP (2006)"},{"issue":"2","key":"41_CR16","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1109\/LSP.2011.2181945","volume":"19","author":"M Kleinsteuber","year":"2012","unstructured":"Kleinsteuber, M., Shen, H.: Blind source separation with compressively sensed linear mixtures. Sig. Process. Lett. 19(2), 107\u2013110 (2012)","journal-title":"Sig. Process. Lett."},{"issue":"3","key":"41_CR17","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1093\/imanum\/22.3.329","volume":"22","author":"NJ Higham","year":"2002","unstructured":"Higham, N.J.: Computing the nearest correlation matrix - a problem from finance. IMA J. Numer. Anal. 22(3), 329\u2013343 (2002)","journal-title":"IMA J. Numer. Anal."},{"issue":"3","key":"41_CR18","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1090\/fim\/002\/05","volume":"3","author":"ST Smith","year":"1994","unstructured":"Smith, S.T.: Optimization techniques on Riemannian manifolds. Fields Inst. Commun. 3(3), 113\u2013135 (1994)","journal-title":"Fields Inst. Commun."},{"key":"41_CR19","volume-title":"Optimization Algorithms on Matrix Manifolds","author":"PA Absil","year":"2009","unstructured":"Absil, P.A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton (2009)"},{"issue":"2","key":"41_CR20","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0895479895290954","volume":"20","author":"A Edelman","year":"1998","unstructured":"Edelman, A., Arias, T.A., Smith, S.T.: The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20(2), 303\u2013353 (1998)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"3","key":"41_CR21","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/s10208-005-0179-9","volume":"7","author":"PA Absil","year":"2007","unstructured":"Absil, P.A., Baker, C.G., Gallivan, K.A.: Trust-region methods on Riemannian manifolds. Found. Comput. Math. 7(3), 303\u2013330 (2007)","journal-title":"Found. Comput. Math."},{"issue":"2","key":"41_CR22","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s10208-006-0221-6","volume":"8","author":"F Alvarez","year":"2008","unstructured":"Alvarez, F., Bolte, J., Munier, J.: A unifying local convergence result for Newton\u2019s method in Riemannian manifolds. Found. Comput. Math. 8(2), 197\u2013226 (2008)","journal-title":"Found. Comput. Math."},{"issue":"1","key":"41_CR23","first-page":"1455","volume":"15","author":"N Boumal","year":"2014","unstructured":"Boumal, N., Mishra, B., Absil, P.A., Sepulchre, R.: Manopt, a Matlab toolbox for optimization on manifolds. JMLR 15(1), 1455\u20131459 (2014)","journal-title":"JMLR"},{"issue":"3","key":"41_CR24","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1145\/1970392.1970395","volume":"58","author":"E Cand\u00e8s","year":"2011","unstructured":"Cand\u00e8s, E., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? J. ACM 58(3), 11 (2011)","journal-title":"J. ACM"},{"key":"41_CR25","doi-asserted-by":"crossref","unstructured":"Ozolin\u0327\u0161, V., Lai, R., Caflisch, R., Osher, S.: Compressed modes for variational problems in mathematics and physics. PNAS 110(46), 18368\u201318373 (2013)","DOI":"10.1073\/pnas.1318679110"},{"issue":"5","key":"41_CR26","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1111\/cgf.12429","volume":"33","author":"T Neumann","year":"2014","unstructured":"Neumann, T., Varanasi, K., Theobalt, C., Magnor, M., Wacker, M.: Compressed manifold modes for mesh processing. Comput. Graphics Forum 33(5), 35\u201344 (2014)","journal-title":"Comput. Graphics Forum"},{"key":"41_CR27","doi-asserted-by":"crossref","unstructured":"Cayton, L., Dasgupta, S.: Robust Euclidean embedding. In: Proceedings of ICML (2006)","DOI":"10.1145\/1143844.1143866"},{"key":"41_CR28","doi-asserted-by":"crossref","unstructured":"Wang, L., Singer, A.: Exact and stable recovery of rotations for robust synchronization. Information and Inference (2013)","DOI":"10.1093\/imaiai\/iat005"},{"issue":"4","key":"41_CR29","first-page":"36","volume":"33","author":"Q Huang","year":"2014","unstructured":"Huang, Q., Wang, F., Guibas, L.: Functional map networks for analyzing and exploring large shape collections. ACM Trans. Graphics 33(4), 36 (2014)","journal-title":"ACM Trans. Graphics"},{"key":"41_CR30","doi-asserted-by":"crossref","unstructured":"Kovnatsky, A., Bronstein, M.M., Bresson, X., Vandergheynst, P.: Functional correspondence by matrix completion. In: Proceedings of CVPR (2015)","DOI":"10.1109\/CVPR.2015.7298692"},{"issue":"1","key":"41_CR31","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s10107-012-0569-0","volume":"134","author":"X Chen","year":"2012","unstructured":"Chen, X.: Smoothing methods for nonsmooth, nonconvex minimization. Math. Program. 134(1), 71\u201399 (2012)","journal-title":"Math. Program."},{"issue":"1","key":"41_CR32","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1023\/A:1022675100677","volume":"97","author":"OP Ferreira","year":"1998","unstructured":"Ferreira, O.P., Oliveira, P.R.: Subgradient algorithm on Riemannian manifolds. J. Optimization Theory Appl. 97(1), 93\u2013104 (1998)","journal-title":"J. Optimization Theory Appl."},{"issue":"8","key":"41_CR33","doi-asserted-by":"publisher","first-page":"3687","DOI":"10.1090\/S0002-9947-07-04075-5","volume":"359","author":"Y Ledyaev","year":"2007","unstructured":"Ledyaev, Y., Zhu, Q.: Nonsmooth analysis on smooth manifolds. Trans. AMS 359(8), 3687\u20133732 (2007)","journal-title":"Trans. AMS"},{"key":"41_CR34","doi-asserted-by":"publisher","first-page":"848","DOI":"10.1016\/j.cam.2013.07.002","volume":"255","author":"PB Borckmans","year":"2014","unstructured":"Borckmans, P.B., Selvan, S.E., Boumal, N., Absil, P.A.: A Riemannian subgradient algorithm for economic dispatch with valve-point effect. J. Comp. Applied Math. 255, 848\u2013866 (2014)","journal-title":"J. Comp. Applied Math."},{"issue":"2","key":"41_CR35","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1007\/s10915-013-9740-x","volume":"58","author":"R Lai","year":"2014","unstructured":"Lai, R., Osher, S.: A splitting method for orthogonality constrained problems. J. Scientific Comput. 58(2), 431\u2013449 (2014)","journal-title":"J. Scientific Comput."},{"key":"41_CR36","unstructured":"Rosman, G., Wang, Y., Tai, X., Kimmel, R., Bruckstein, A.M.: Fast regularization of matrix-valued images. In: Proceedings of Efficient Algorithms for Global Optimization Methods in Computer Vision (2011)"},{"issue":"1","key":"41_CR37","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/0898-1221(76)90003-1","volume":"2","author":"D Gabay","year":"1976","unstructured":"Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput. Math. Appl. 2(1), 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"key":"41_CR38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2010","unstructured":"Boyd, S., Parikk, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3, 1\u2013122 (2010)","journal-title":"Found. Trends Mach. Learn."},{"issue":"5","key":"41_CR39","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF00927673","volume":"4","author":"MR Hestenes","year":"1969","unstructured":"Hestenes, M.R.: Multiplier and gradient methods. J. Optim. Theory Appl. 4(5), 303\u2013320 (1969)","journal-title":"J. Optim. Theory Appl."},{"key":"41_CR40","unstructured":"Powell, M.J.D.: A method for nonlinear constraints in minimization problems. In: Optimization. Academic Press, London, New York (1969)"},{"key":"41_CR41","volume-title":"Constrained Optimization and Lagrange Multiplier Methods","author":"DP Bertsekas","year":"1982","unstructured":"Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York (1982)"},{"issue":"4","key":"41_CR42","doi-asserted-by":"publisher","first-page":"1286","DOI":"10.1137\/060654797","volume":"18","author":"R Andreani","year":"2007","unstructured":"Andreani, R., Birgin, E.G., Mart\u00ednez, J.M., Schuverdt, M.L.: On augmented Lagrangian methods with general lower-level constraints. SIAM J. Optimization 18(4), 1286\u20131309 (2007)","journal-title":"SIAM J. Optimization"},{"issue":"2","key":"41_CR43","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1287\/moor.1100.0449","volume":"35","author":"H Attouch","year":"2010","unstructured":"Attouch, H., Bolte, J., Redont, P., Soubeyran, A.: Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-Lojasiewicz inequality. Math. Oper. Res. 35(2), 438\u2013457 (2010)","journal-title":"Math. Oper. Res."},{"key":"41_CR44","unstructured":"Wang, Y., Wotao, Y., Jinshan, Z.: Global Convergence of ADMM in Nonconvex Nonsmooth Optimization (2015). arXiv:1511.06324"},{"key":"41_CR45","unstructured":"Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: Proceedings of NIPS (2002)"},{"key":"41_CR46","doi-asserted-by":"crossref","unstructured":"Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Proceedings of NIPS (2001)","DOI":"10.7551\/mitpress\/1120.003.0080"},{"issue":"4","key":"41_CR47","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2185520.2185526","volume":"31","author":"M Ovsjanikov","year":"2012","unstructured":"Ovsjanikov, M., Ben-Chen, M., Solomon, J., Butscher, A., Guibas, L.J.: Functional maps: a flexible representation of maps between shapes. ACM Trans. Graphics 31(4), 1\u201311 (2012)","journal-title":"ACM Trans. Graphics"},{"key":"41_CR48","volume-title":"Numerical Geometry of Non-rigid Shapes","author":"AM Bronstein","year":"2008","unstructured":"Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Numerical Geometry of Non-rigid Shapes. Springer, New York (2008)"},{"key":"41_CR49","first-page":"79","volume":"30","author":"VG Kim","year":"2011","unstructured":"Kim, V.G., Lipman, Y., Funkhouser, T.: Blended intrinsic maps. Trans. Graphics 30, 79 (2011)","journal-title":"Trans. Graphics"},{"key":"41_CR50","doi-asserted-by":"crossref","unstructured":"Bekkerman, R., Jeon, J.: Multi-modal clustering for multimedia collections. In: Proceedings of CVPR (2007)","DOI":"10.1109\/CVPR.2007.383223"},{"key":"41_CR51","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809071","volume-title":"Introduction to Information Retrieval","author":"CD Manning","year":"2008","unstructured":"Manning, C.D., Raghavan, P., Sch\u00fctze, H.: Introduction to Information Retrieval. Cambridge University Press, Cambridge (2008)"},{"key":"41_CR52","unstructured":"Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: Proceedings of NIPS (2001)"},{"key":"41_CR53","series-title":"Lecture Notes in Control and Information Sciences","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/978-1-84800-155-8_7","volume-title":"Recent Advances in Learning and Control","author":"M Grant","year":"2008","unstructured":"Grant, M., Boyd, S.: Graph implementations for nonsmooth convex programs. In: Blondel, V., Boyd, S., Kimura, H. (eds.) Recent Advances in Learning and Control. LNCIS, vol. 371, pp. 95\u2013110. Springer, Heidelberg (2008)"}],"container-title":["Lecture Notes in Computer Science","Computer Vision \u2013 ECCV 2016"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-46454-1_41","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T11:05:04Z","timestamp":1718795104000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-46454-1_41"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319464534","9783319464541"],"references-count":53,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-46454-1_41","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"16 September 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ECCV","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"European Conference on Computer Vision","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Amsterdam","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"The Netherlands","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2016","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 October 2016","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 October 2016","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"eccv2016","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.eccv2016.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}