{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T08:43:47Z","timestamp":1774946627528,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":39,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642238079","type":"print"},{"value":"9783642238086","type":"electronic"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-23808-6_20","type":"book-chapter","created":{"date-parts":[[2011,8,18]],"date-time":"2011-08-18T03:40:29Z","timestamp":1313638829000},"page":"305-317","source":"Crossref","is-referenced-by-count":14,"title":["Fast Projections onto \u21131,q -Norm Balls for Grouped Feature Selection"],"prefix":"10.1007","author":[{"given":"Suvrit","family":"Sra","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"20_CR1","unstructured":"Bach, F.: Structured sparsity-inducing norms through submodular functions. In: NIPS (2010)"},{"key":"20_CR2","volume-title":"Optimization for Machine Learning","author":"F. Bach","year":"2011","unstructured":"Bach, F., Jenatton, R., Mairal, J., Obozinski, G.: Convex optimization with sparsity-inducing norms. In: Sra, S., Nowozin, S., Wright, S.J. (eds.) Optimization for Machine Learning. MIT Press, Cambridge (2011)"},{"key":"20_CR3","first-page":"1179","volume":"9","author":"F.R. Bach","year":"2008","unstructured":"Bach, F.R.: Consistency of the Group Lasso and Multiple Kernel Learning. J. Mach. Learn. Res.\u00a09, 1179\u20131225 (2008)","journal-title":"J. Mach. Learn. Res."},{"issue":"1","key":"20_CR4","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1093\/imanum\/8.1.141","volume":"8","author":"J. Barzilai","year":"1988","unstructured":"Barzilai, J., Borwein, J.M.: Two-Point Step Size Gradient Methods. IMA Journal of Numerical Analysis\u00a08(1), 141\u2013148 (1988)","journal-title":"IMA Journal of Numerical Analysis"},{"key":"20_CR5","unstructured":"van den Berg, E., Schmidt, M., Friedlander, M.P., Murphy, K.: Group sparsity via linear-time projection. Tech. Rep. TR-2008-09, Univ. British Columbia (June 2008)"},{"key":"20_CR6","volume-title":"Nonlinear Programming","author":"D.P. Bertsekas","year":"1999","unstructured":"Bertsekas, D.P.: Nonlinear Programming, 2nd edn. Athena Scientific, Belmon (1999)","edition":"2"},{"issue":"4","key":"20_CR7","doi-asserted-by":"publisher","first-page":"1196","DOI":"10.1137\/S1052623497330963","volume":"10","author":"E.G. Birgin","year":"2000","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Raydan, M.: Nonmonotone Spectral Projected Gradient Methods on Convex Sets. SIAM J. Opt.\u00a010(4), 1196\u20131211 (2000)","journal-title":"SIAM J. Opt."},{"key":"20_CR8","doi-asserted-by":"crossref","unstructured":"Combettes, P.L., Pesquet, J.: Proximal Splitting Methods in Signal Processing. arXiv:0912.3522v4 (May 2010)","DOI":"10.1007\/978-1-4419-9569-8_10"},{"issue":"1","key":"20_CR9","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s00211-004-0569-y","volume":"100","author":"Y.H. Dai","year":"2005","unstructured":"Dai, Y.H., Fletcher, R.: Projected Barzilai-Borwein Methods for Large-scale Box-constrained Quadratic Programming. Numerische Mathematik\u00a0100(1), 21\u201347 (2005)","journal-title":"Numerische Mathematik"},{"issue":"3","key":"20_CR10","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1109\/18.382009","volume":"41","author":"D. Donoho","year":"2002","unstructured":"Donoho, D.: Denoising by soft-thresholding. IEEE Tran. Inf. Theory\u00a041(3), 613\u2013627 (2002)","journal-title":"IEEE Tran. Inf. Theory"},{"key":"20_CR11","unstructured":"Duchi, J., Singer, Y.: Online and Batch Learning using Forward-Backward Splitting. JMLR (September 2009)"},{"key":"20_CR12","first-page":"615","volume":"6","author":"T. Evgeniou","year":"2005","unstructured":"Evgeniou, T., Micchelli, C., Pontil, M.: Learning multiple tasks with kernel methods. J. Mach. Learn. Res.\u00a06, 615\u2013637 (2005)","journal-title":"J. Mach. Learn. Res."},{"key":"20_CR13","doi-asserted-by":"crossref","unstructured":"Evgeniou, T., Pontil, M.: Regularized multi-task learning. In: KDD (2004)","DOI":"10.1145\/1014052.1014067"},{"key":"20_CR14","unstructured":"Friedman, J., Hastie, T., Tibshirani, R.: A note on the group lasso and a sparse group lasso. arXiv:1001.0736v1 [math.ST] (January 2010)"},{"key":"20_CR15","unstructured":"Jenatton, R., Mairal, J., Obozinski, G., Bach, F.: Proximal Methods for Sparse Hierarchical Dictionary Learning. In: ICML (2010)"},{"key":"20_CR16","unstructured":"Kim, D., Sra, S., Dhillon, I.S.: A scalable trust-region algorithm with application to mixed-norm regression. In: Int. Conf. Machine Learning (ICML) (2010)"},{"key":"20_CR17","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1007\/s10957-007-9259-0","volume":"134","author":"K. Kiwiel","year":"2007","unstructured":"Kiwiel, K.: On Linear-Time Algorithms for the Continuous Quadratic Knapsack Problem. Journal of Optimization Theory and Applications\u00a0134, 549\u2013554 (2007)","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"3","key":"20_CR18","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/j.acha.2009.05.006","volume":"27","author":"M. Kowalski","year":"2009","unstructured":"Kowalski, M.: Sparse regression using mixed norms. Applied and Computational Harmonic Analysis\u00a027(3), 303\u2013324 (2009)","journal-title":"Applied and Computational Harmonic Analysis"},{"key":"20_CR19","doi-asserted-by":"crossref","unstructured":"Liu, H., Palatucci, M., Zhang, J.: Blockwise Coordinate Descent Procedures for the Multi-task Lasso, with Applications to Neural Semantic Basis Discovery. In: Int. Conf. Machine Learning (June 2009)","DOI":"10.1145\/1553374.1553458"},{"key":"20_CR20","unstructured":"Liu, J., Ji, S., Ye, J.: SLEP: Sparse Learning with Efficient Projections. Arizona State University (2009), http:\/\/www.public.asu.edu\/~jye02\/Software\/SLEP"},{"key":"20_CR21","unstructured":"Liu, J., Ye, J.: Efficient L1\/Lq Norm Regularization. arXiv:1009.4766v1 (2010)"},{"key":"20_CR22","unstructured":"Liu, J., Ye, J.: Moreau-Yosida Regularization for Grouped Tree Structure Learning. In: NIPS (2010)"},{"key":"20_CR23","doi-asserted-by":"crossref","unstructured":"Liu, J., Ye, J.: Efficient Euclidean projections in linear time. In: ICML (June 2009)","DOI":"10.1145\/1553374.1553459"},{"key":"20_CR24","unstructured":"Mairal, J., Jenatton, R., Obozinski, G., Bach, F.: Network Flow Algorithms for Structured Sparsity. In: NIPS (2010)"},{"issue":"1","key":"20_CR25","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/BF00938486","volume":"50","author":"C. Michelot","year":"1986","unstructured":"Michelot, C.: A finite algorithm for finding the projection of a point onto the canonical simplex of \u211d n . J. Optim. Theory Appl.\u00a050(1), 195\u2013200 (1986)","journal-title":"J. Optim. Theory Appl."},{"key":"20_CR26","unstructured":"Obonzinski, G., Taskar, B., Jordan, M.: Multi-task feature selection. Tech. rep., UC Berkeley (June 2006)"},{"key":"20_CR27","unstructured":"Patriksson, M.: A survey on a classic core problem in operations research. Tech. Rep. 2005:33, Chalmers University of Technology and G\u00f6teborg University (October 2005)"},{"key":"20_CR28","doi-asserted-by":"crossref","unstructured":"Quattoni, A., Carreras, X., Collins, M., Darrell, T.: An Efficient Projection for \u21131,\u2009\u221e\u2009 Regularization. In: ICML (2009)","DOI":"10.1145\/1553374.1553484"},{"key":"20_CR29","unstructured":"Rakotomamonjy, A., Flamary, R., Gasso, G., Canu, S.: \u2113 p \u2009\u2212\u2009\u2113 q penalty for sparse linear and sparse multiple kernel multi-task learning. Tech. Rep. hal-00509608, version 1, INSA-Rouen (2010)"},{"key":"20_CR30","unstructured":"Rice, U.: Compressive sensing resources (October 2010), http:\/\/dsp.rice.edu\/cs"},{"key":"20_CR31","unstructured":"Rish, I., Grabarnik, G.: Sparse modeling: ICML 2010 tutorial. Online (June 2010)"},{"key":"20_CR32","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"R.T. Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton Univ. Press, Princeton (1970)"},{"key":"20_CR33","unstructured":"Schmidt, M., van den Berg, E., Friedlander, M., Murphy, K.: Optimizing Costly Functions with Simple Constraints: A Limited-Memory Projected Quasi-Newton Algorithm. In: AISTATS (2009)"},{"issue":"1","key":"20_CR34","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1016\/j.csda.2007.01.025","volume":"52","author":"T. Simil\u00e4","year":"2007","unstructured":"Simil\u00e4, T., Tikka, J.: Input selection and shrinkage in multiresponse linear regression. Comp. Stat. & Data Analy.\u00a052(1), 406\u2013422 (2007)","journal-title":"Comp. Stat. & Data Analy."},{"issue":"3","key":"20_CR35","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1016\/j.sigpro.2005.05.031","volume":"86","author":"J.A. Tropp","year":"2006","unstructured":"Tropp, J.A.: Algorithms for simultaneous sparse approximation, Part II: Convex relaxation. Signal Proc.\u00a086(3), 589\u2013602 (2006)","journal-title":"Signal Proc."},{"key":"20_CR36","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1198\/004017005000000139","volume":"27","author":"B.A. Turlach","year":"2005","unstructured":"Turlach, B.A., Venables, W.N., Wright, S.J.: Simultaneous Variable Selection. Technometrics\u00a027, 349\u2013363 (2005)","journal-title":"Technometrics"},{"key":"20_CR37","unstructured":"Yuan, M., Lin, Y.: Model Selection and Estimation in Regression with Grouped Variables. Tech. Rep. 1095, Univ. of Wisconsin, Dept. of Stat. (2004)"},{"key":"20_CR38","unstructured":"Zhang, Y., Yeung, D.Y., Xu, Q.: Probabilistic Multi-Task Feature Selection. In: NIPS (2010)"},{"issue":"6A","key":"20_CR39","doi-asserted-by":"publisher","first-page":"3468","DOI":"10.1214\/07-AOS584","volume":"37","author":"P. Zhao","year":"2009","unstructured":"Zhao, P., Rocha, G., Yu, B.: The composite absolute penalties family for grouped and hierarchical variable selection. Ann. Stat.\u00a037(6A), 3468\u20133497 (2009)","journal-title":"Ann. Stat."}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Knowledge Discovery in Databases"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-23808-6_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:48:35Z","timestamp":1560473315000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-23808-6_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642238079","9783642238086"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-23808-6_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011]]}}}