{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T06:48:40Z","timestamp":1767422920309,"version":"3.40.4"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,1,11]],"date-time":"2014-01-11T00:00:00Z","timestamp":1389398400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2014,10]]},"DOI":"10.1007\/s10915-013-9815-8","type":"journal-article","created":{"date-parts":[[2014,1,10]],"date-time":"2014-01-10T15:17:56Z","timestamp":1389367076000},"page":"17-41","source":"Crossref","is-referenced-by-count":16,"title":["Nonmonotone Barzilai\u2013Borwein Gradient Algorithm for $$\\ell _{1}$$ \u2113 1 -Regularized Nonsmooth Minimization in Compressive Sensing"],"prefix":"10.1007","volume":"61","author":[{"given":"Yunhai","family":"Xiao","sequence":"first","affiliation":[]},{"given":"Soon-Yi","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Liqun","family":"Qi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,1,11]]},"reference":[{"key":"9815_CR1","doi-asserted-by":"crossref","unstructured":"Andrew, G., Gao, J.: Scalable training of $$\\ell _{1}$$ \u2113 1 -regularized log-linear models. In: Proceedings of the Twenty Fourth International Conference on Machine Learning, (ICML) (2007)","DOI":"10.1145\/1273496.1273501"},{"key":"9815_CR2","doi-asserted-by":"crossref","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 method. IMA J. Numer. Anal. 8, 141\u2013148 (1988)","journal-title":"IMA J. Numer. Anal."},{"key":"9815_CR3","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183\u2013202 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"9815_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/090756855","volume":"4","author":"S Becker","year":"2011","unstructured":"Becker, S., Bobin, J., Cand\u00e8s, E.: NESTA: a fast and accurate first-order method for sparse recovery. SIAM J. Imaging Sci. 4, 1\u201339 (2011)","journal-title":"SIAM J. Imaging Sci."},{"key":"9815_CR5","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1137\/S1052623497330963","volume":"10","author":"EG Birgin","year":"2000","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Raydan, M.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10, 1196\u20131211 (2000)","journal-title":"SIAM J. Optim."},{"key":"9815_CR6","doi-asserted-by":"crossref","first-page":"2992","DOI":"10.1109\/TIP.2007.909319","volume":"16","author":"JM Bioucas-Dias","year":"2007","unstructured":"Bioucas-Dias, J.M., Figueiredo, M.: A new TwIST: two-step iterative shrinkage\/thresholding algorithms for image restoratin. IEEE Trans. Image Process. 16, 2992\u20133004 (2007)","journal-title":"IEEE Trans. Image Process."},{"key":"9815_CR7","doi-asserted-by":"crossref","first-page":"1956","DOI":"10.1137\/080738970","volume":"20","author":"JF Cai","year":"2010","unstructured":"Cai, J.F., Cand\u00e8s, E., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20, 1956\u20131982 (2010)","journal-title":"SIAM J. Optim."},{"key":"9815_CR8","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s10208-004-0162-x","volume":"6","author":"E Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E., Romberg, J.: Quantitative robust uncertainty principles and optimally sparse decompositions. Found. Comput. Math. 6, 227\u2013254 (2006)","journal-title":"Found. Comput. Math."},{"key":"9815_CR9","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1002\/cpa.20124","volume":"59","author":"E Cand\u00e8s","year":"2005","unstructured":"Cand\u00e8s, E., Romberg, J., Tao, T.: Stable signal recovery from imcomplete and inaccurate information. Commun. Pure Appl. Math. 59, 1207\u20131233 (2005)","journal-title":"Commun. Pure Appl. Math."},{"key":"9815_CR10","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/TIT.2005.862083","volume":"52","author":"E Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequence information. IEEE Trans. Inf. Theory 52, 489\u2013509 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9815_CR11","doi-asserted-by":"crossref","first-page":"5406","DOI":"10.1109\/TIT.2006.885507","volume":"52","author":"E Cand\u00e8s","year":"2004","unstructured":"Cand\u00e8s, E., Tao, T.: Near optimal signal recovery from random projections: universal encoding strategies. IEEE Trans. Inf. Theory 52, 5406\u20135425 (2004)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9815_CR12","first-page":"1369","volume":"9","author":"KW Chang","year":"2008","unstructured":"Chang, K.W., Hsieh, C.J., Lin, C.J.: Coordinate descent method for large-scale L2-loss linear SVM. J. Mach. Learn. Res. 9, 1369\u20131398 (2008)","journal-title":"J. Mach. Learn. Res."},{"key":"9815_CR13","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1093\/imanum\/drn019","volume":"29","author":"W Cheng","year":"2009","unstructured":"Cheng, W., Li, D.H.: A derivative-free nonmonotone line search and its application to the spectral residual method. IMA J. Numer. Anal. 29, 814\u2013825 (2009)","journal-title":"IMA J. Numer. Anal."},{"key":"9815_CR14","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1145\/200979.201043","volume":"21","author":"AR Conn","year":"1995","unstructured":"Conn, A.R., Gould, N.I.M., Toint, PhL: CUTE: constrained and unconstrained testing environment. ACM Trans. Math. Softw. 21, 123\u2013160 (1995)","journal-title":"ACM Trans. Math. Softw."},{"key":"9815_CR15","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/s10107-004-0516-9","volume":"103","author":"YH Dai","year":"2005","unstructured":"Dai, Y.H., Fletcher, R.: On the asymptotic behaviour of some new gradient methods. Math. Program. 103, 541\u2013559 (2005)","journal-title":"Math. Program."},{"key":"9815_CR16","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1093\/imanum\/drl006","volume":"26","author":"YH Dai","year":"2006","unstructured":"Dai, Y.H., Hager, W.W., Schittkowski, K., Zhang, H.C.: The cyclic Barzilai\u2013Borwein method for unconstrained optimization. IMA J. Numer. Anal. 26, 604\u2013627 (2006)","journal-title":"IMA J. Numer. Anal."},{"key":"9815_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/imanum\/22.1.1","volume":"26","author":"YH Dai","year":"2002","unstructured":"Dai, Y.H., Liao, L.Z.: R-linear convergence of the Barzilai and Borwein gradient method. IMA J. Numer. Anal. 26, 1\u201310 (2002)","journal-title":"IMA J. Numer. Anal."},{"key":"9815_CR18","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"DL Donoho","year":"2006","unstructured":"Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52, 1289\u20131306 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9815_CR19","first-page":"2899","volume":"10","author":"J Duchi","year":"2009","unstructured":"Duchi, J., Singer, Y.: Efficient online and batch learning using forward backword splitting. J. Mach. Learn. Res. 10, 2899\u20132934 (2009)","journal-title":"J. Mach. Learn. Res."},{"key":"9815_CR20","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1109\/JSTSP.2007.910281","volume":"1","author":"M Figueiredo","year":"2007","unstructured":"Figueiredo, M., Nowak, R.D., Wright, S.J.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process 1, 586\u2013597 (2007)","journal-title":"IEEE J. Sel. Top. Signal Process"},{"key":"9815_CR21","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1198\/004017007000000245","volume":"49","author":"A Genkin","year":"2007","unstructured":"Genkin, A., Lewis, D.D., Madigan, D.: Large-scale Bayesian logistic regression for text categorization. Technometrices 49, 291\u2013304 (2007)","journal-title":"Technometrices"},{"key":"9815_CR22","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1137\/0723046","volume":"23","author":"L Grippo","year":"1986","unstructured":"Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search technique for Newton\u2019s method. SIAM J. Numer. Anal. 23, 707\u2013716 (1986)","journal-title":"SIAM J. Numer. Anal."},{"key":"9815_CR23","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1137\/070698920","volume":"19","author":"ET Hale","year":"2008","unstructured":"Hale, E.T., Yin, W., Zhang, Y.: Fixed-point continuation for $$\\ell _{1}$$ \u2113 1 -minimization: methodology and convergence. SIAM J. Optim. 19, 1107\u20131130 (2008)","journal-title":"SIAM J. Optim."},{"key":"9815_CR24","unstructured":"Kim, S., Koh, K., Lustig, M., Boyd, S., Gorinevsky, D.: An interior-point method for large-scale $$\\ell _{1}$$ \u2113 1 -regularized least squares. IEEE J. Sel. Top. Signal Process. 1, 606\u2013617 (2007)"},{"key":"9815_CR25","first-page":"1519","volume":"8","author":"K Koh","year":"2007","unstructured":"Koh, K., Kim, S., Boyd, S.: An interior-point method for large-scale $$\\ell _{1}$$ \u2113 1 -regularized logistic regression. J. Mach. Learn. Res. 8, 1519\u20131555 (2007)","journal-title":"J. Mach. Learn. Res."},{"key":"9815_CR26","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1137\/S1052623498345075","volume":"9","author":"CJ Lin","year":"1999","unstructured":"Lin, C.J., Mor\u00e9, J.J.: Newton\u2019s method for large-scale bound constrained problems. SIAM J. Optim. 9, 1100\u20131127 (1999)","journal-title":"SIAM J. Optim."},{"key":"9815_CR27","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s10107-011-0452-4","volume":"135","author":"Z Lu","year":"2012","unstructured":"Lu, Z., Zhang, Y.: An augmented Lagrangian approach for sparse principal component analysis. Math. Program. 135, 149\u2013193 (2012)","journal-title":"Math. Program."},{"key":"9815_CR28","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10107-004-0552-5","volume":"103","author":"Y Nesterov","year":"2005","unstructured":"Nesterov, Y.: Smooth minimization of non-smooth functions. Math. Program. 103, 127\u2013152 (2005)","journal-title":"Math. Program."},{"key":"9815_CR29","unstructured":"Nesterov, Y.: Gradient methods for minimizing composite objective function, ECORE Discussion Paper 2007\/76. http:\/\/www.ecore.be\/DPs\/dp_1191313936.pdf (2007)"},{"key":"9815_CR30","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1090\/S0025-5718-1980-0572855-7","volume":"35","author":"J Nocedal","year":"1980","unstructured":"Nocedal, J.: Updating quasi-Newton matrices with limited storage. Math. Comput. 35, 773\u2013782 (1980)","journal-title":"Math. Comput."},{"key":"9815_CR31","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1093\/imanum\/13.3.321","volume":"13","author":"M Raydan","year":"1993","unstructured":"Raydan, M.: On the Barzilai and Borwein choice of steplength for the gradient method. IMA J. Numer. Anal. 13, 321\u2013326 (1993)","journal-title":"IMA J. Numer. Anal."},{"key":"9815_CR32","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1137\/S1052623494266365","volume":"7","author":"M Raydan","year":"1997","unstructured":"Raydan, M.: The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Optim. 7, 26\u201333 (1997)","journal-title":"SIAM J. Optim."},{"key":"9815_CR33","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1137\/070697835","volume":"52","author":"B Recht","year":"2010","unstructured":"Recht, B., Fazel, M., Parrilo, P.A.: Guaranteed minimum rank solutions of matrix equations via nuclear norm minimization. SIAM Rev. 52, 471\u2013501 (2010)","journal-title":"SIAM Rev."},{"key":"9815_CR34","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"L Rudin","year":"1992","unstructured":"Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D Nonlinear Phenom. 60, 259\u2013268 (1992)","journal-title":"Phys. D Nonlinear Phenom."},{"key":"9815_CR35","doi-asserted-by":"crossref","unstructured":"Shalev-Shwartz, S., Tewari, A.: Stochastic method for l1 regularized loss minimization. In: Proceedings of the Twenty Sixth International Conference on Machine Learning (ICML) (2009)","DOI":"10.1145\/1553374.1553493"},{"key":"9815_CR36","first-page":"713","volume":"11","author":"J Shi","year":"2010","unstructured":"Shi, J., Yin, W., Osher, S., Sajda, P.: A fast hybrid algorithm for large-scale $$\\ell _{1}$$ \u2113 1 -regularized logistic regression. J. Mach. Learn. Res. 11, 713\u2013741 (2010)","journal-title":"J. Mach. Learn. Res."},{"key":"9815_CR37","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/s10107-007-0170-0","volume":"117","author":"P Tseng","year":"2009","unstructured":"Tseng, P., Yun, S.: A coordinate gradient descent method for nonsmooth separable minimization. Math. Program. 117, 387\u2013423 (2009)","journal-title":"Math. Program."},{"key":"9815_CR38","unstructured":"van den Berg, E., Friedlander, M.P.: Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31, 890\u2013912 (2008)"},{"key":"9815_CR39","doi-asserted-by":"crossref","first-page":"1832","DOI":"10.1137\/090747695","volume":"32","author":"Z Wen","year":"2010","unstructured":"Wen, Z., Yin, W., Goldfarb, D., Zhang, Y.: A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization, and continuation. SIAM J. Sci. Comput. 32, 1832\u20131857 (2010)","journal-title":"SIAM J. Sci. Comput."},{"key":"9815_CR40","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1080\/10556788.2011.591398","volume":"27","author":"Z Wen","year":"2012","unstructured":"Wen, Z., Yin, W., Zhang, H., Goldfarb, D.: On the convergence of an active-set method for $$\\ell _{1}$$ \u2113 1 minimization. Optim. Method Softw 27, 1127\u20131146 (2012)","journal-title":"Optim. Method Softw"},{"key":"9815_CR41","doi-asserted-by":"crossref","unstructured":"Wright, S.J., Nowak, R.D., Figueiredo, M.A.T.: Sparse reconstruction by separable approximation. In: Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, pp 3373\u20133376 (2008)","DOI":"10.1109\/ICASSP.2008.4518374"},{"key":"9815_CR42","first-page":"1","volume":"5","author":"J Wright","year":"2009","unstructured":"Wright, J., Ma, Y., Ganesh, A., Rao, S.: Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization. J. ACM 5, 1\u201344 (2009)","journal-title":"J. ACM"},{"key":"9815_CR43","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1137\/090777761","volume":"33","author":"J Yang","year":"2011","unstructured":"Yang, J., Zhang, Y.: Alternating direction algorithms for $$\\ell _{1}$$ \u2113 1 -problems in compressive sensing. SIAM J. Sci. Comput. 33, 250\u2013278 (2011)","journal-title":"SIAM J. Sci. Comput."},{"key":"9815_CR44","first-page":"1145","volume":"11","author":"J Yu","year":"2010","unstructured":"Yu, J., Vishwanathan, S.V.N., G\u00fcnter, S., Schraudolph, N.N.: A quasi-Newton approach to nonsmooth convex optimization problems in machine learning. J. Mach. Learn. Res. 11, 1145\u20131200 (2010)","journal-title":"J. Mach. Learn. Res."},{"key":"9815_CR45","first-page":"3183","volume":"11","author":"GX Yuan","year":"2010","unstructured":"Yuan, G.X., Chang, K.W., Hsieh, C.J., Lin, C.J.: A comparison of optimization methods and software for large-scale $$\\ell _{1}$$ \u2113 1 -regularized linear classification. J. Mach. Learn. Res. 11, 3183\u20133234 (2010)","journal-title":"J. Mach. Learn. Res."},{"key":"9815_CR46","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/s10915-011-9507-1","volume":"51","author":"X Yuan","year":"2012","unstructured":"Yuan, X.: Alternating direction method for covariance selection models. J. Sci. Comput. 51, 261\u2013273 (2012)","journal-title":"J. Sci. Comput."},{"key":"9815_CR47","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s10589-009-9251-8","volume":"48","author":"S Yun","year":"2011","unstructured":"Yun, S., Toh, K.C.: A coordinate gradient descent method for $$\\ell _{1}$$ \u2113 1 -regularized convex minimization. Comput. Optim. Appl. 48, 273\u2013307 (2011)","journal-title":"Comput. Optim. Appl."},{"key":"9815_CR48","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1137\/S1052623403428208","volume":"14","author":"H Zhang","year":"2004","unstructured":"Zhang, H., Hager, W.W.: A nonmonotone line search technique and its application to unconstrained optimization. SIAM J. Optim. 14, 1043\u20131056 (2004)","journal-title":"SIAM J. Optim."},{"key":"9815_CR49","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1142\/S0217595910002582","volume":"27","author":"Y Zhang","year":"2010","unstructured":"Zhang, Y., Sun, W., Qi, L.: A nonmonotone filter Barzilai-Borwein method for optimization. Asia Pac. J. Oper. Res. 27, 55\u201369 (2010)","journal-title":"Asia Pac. J. Oper. Res."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9815-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-013-9815-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9815-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T13:48:26Z","timestamp":1746107306000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-013-9815-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,11]]},"references-count":49,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,10]]}},"alternative-id":["9815"],"URL":"https:\/\/doi.org\/10.1007\/s10915-013-9815-8","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2014,1,11]]}}}