{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T08:02:50Z","timestamp":1751961770095},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2015,2,18]],"date-time":"2015-02-18T00:00:00Z","timestamp":1424217600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2015,7]]},"DOI":"10.1007\/s10589-015-9732-x","type":"journal-article","created":{"date-parts":[[2015,2,17]],"date-time":"2015-02-17T08:48:35Z","timestamp":1424162915000},"page":"609-634","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Path following in the exact penalty method of convex programming"],"prefix":"10.1007","volume":"61","author":[{"given":"Hua","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenneth","family":"Lange","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,2,18]]},"reference":[{"key":"9732_CR1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"S Boyd","year":"2004","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)"},{"key":"9732_CR2","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1137\/S0036144502414942","volume":"44","author":"A Forsgren","year":"2002","unstructured":"Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Rev. 44, 525\u2013597 (2002)","journal-title":"SIAM Rev."},{"key":"9732_CR3","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1007\/978-0-387-74503-9","volume-title":"Linear and Nonlinear Programming. International Series in Operations Research & Management Science","author":"DG Luenberger","year":"2008","unstructured":"Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming. International Series in Operations Research & Management Science, 3rd edn, p. 116. Springer, New York (2008)","edition":"3"},{"key":"9732_CR4","volume-title":"Numerical Optimization. Springer Series in Operations Research and Financial Engineering","author":"J Nocedal","year":"2006","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization. Springer Series in Operations Research and Financial Engineering, 2nd edn. Springer, New York (2006)","edition":"2"},{"key":"9732_CR5","doi-asserted-by":"crossref","DOI":"10.1515\/9781400841059","volume-title":"Nonlinear Optim.","author":"A Ruszczy\u0144ski","year":"2006","unstructured":"Ruszczy\u0144ski, A.: Nonlinear Optim. Princeton University Press, Princeton (2006)"},{"issue":"5","key":"9732_CR6","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1287\/mnsc.13.5.344","volume":"13","author":"WI Zangwill","year":"1967","unstructured":"Zangwill, W.I.: Non-linear programming via penalty functions. Manag. Sci. 13(5), 344\u2013358 (1967)","journal-title":"Manag. Sci."},{"key":"9732_CR7","unstructured":"Hestenes, M.R.: Optimization Theory: The Finite Dimensional Case. Wiley-Interscience (Wiley), New York (1975)"},{"key":"9732_CR8","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1080\/10618600.2012.681248","volume":"22","author":"H Zhou","year":"2013","unstructured":"Zhou, H., Lange, K.: A path algorithm for constrained estimation. J. Comput. Gr. Stat. 22, 261\u2013283 (2013)","journal-title":"J. Comput. Gr. Stat."},{"key":"9732_CR9","volume-title":"The Linear Complementarity Problem. Computer Science and Scientific Computing","author":"RW Cottle","year":"1992","unstructured":"Cottle, R.W., Pang, J.-S., Stone, R.E.: The Linear Complementarity Problem. Computer Science and Scientific Computing. Academic Press Inc., Boston (1992)"},{"issue":"4","key":"9732_CR10","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1137\/1028157","volume":"28","author":"LT Watson","year":"1986","unstructured":"Watson, L.T.: Numerical linear algebra aspects of globally convergent homotopy methods. SIAM Rev. 28(4), 529\u2013545 (1986)","journal-title":"SIAM Rev."},{"key":"9732_CR11","doi-asserted-by":"crossref","unstructured":"Watson, L.T.: Theory of globally convergent probability-one homotopies for nonlinear programming. SIAM J. Optim., 11(3), 761\u2013780, electronic (2000\/2001)","DOI":"10.1137\/S105262349936121X"},{"key":"9732_CR12","volume-title":"Pathways to Solutions, Fixed Points, and Equilibria. Prentice-Hall Series in Computational Mathematics","author":"WI Zangwill","year":"1981","unstructured":"Zangwill, W.I., Garcia, C.B.: Pathways to Solutions, Fixed Points, and Equilibria. Prentice-Hall Series in Computational Mathematics. Prentice-Hall, New Jersey (1981)"},{"issue":"506","key":"9732_CR13","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1080\/01621459.2013.864166","volume":"109","author":"H Zhou","year":"2014","unstructured":"Zhou, H., Wu, Y.: A generic path algorithm for regularized statistical estimation. J. Am. Statist. Assoc. 109(506), 686\u2013699 (2014)","journal-title":"J. Am. Statist. Assoc."},{"key":"9732_CR14","unstructured":"Bertsekas, D.P.: Convex Analysis and Optimization. Athena Scientific, Belmont. With Angelia Nedi\u0107 and Asuman E. Ozdaglar (2003)"},{"issue":"2","key":"9732_CR15","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1214\/009053604000000067","volume":"32","author":"B Efron","year":"2004","unstructured":"Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. Ann. Stat. 32(2), 407\u2013499 (2004). (with discussion, and a rejoinder by the authors)","journal-title":"Ann. Stat."},{"issue":"3","key":"9732_CR16","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1093\/imanum\/20.3.389","volume":"20","author":"MR Osborne","year":"2000","unstructured":"Osborne, M.R., Presnell, B., Turlach, B.A.: A new approach to variable selection in least squares problems. IMA J. Numer. Anal. 20(3), 389\u2013403 (2000)","journal-title":"IMA J. Numer. Anal."},{"issue":"3","key":"9732_CR17","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1214\/11-AOS878","volume":"39","author":"RJ Tibshirani","year":"2011","unstructured":"Tibshirani, R.J., Taylor, J.: The solution path of the generalized lasso. Ann. Stat. 39(3), 1335\u20131371 (2011)","journal-title":"Ann. Stat."},{"key":"9732_CR18","volume-title":"Optimization. Springer Texts in Statistics","author":"K Lange","year":"2004","unstructured":"Lange, K.: Optimization. Springer Texts in Statistics. Springer, New York (2004)"},{"key":"9732_CR19","volume-title":"Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley Series in Probability and Statistics","author":"JR Magnus","year":"1999","unstructured":"Magnus, J.R., Neudecker, H.: Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley Series in Probability and Statistics. Wiley, Chichester (1999)"},{"key":"9732_CR20","doi-asserted-by":"crossref","unstructured":"Lange, K.: Numerical Analysis for Statisticians. Statistics and Computing, 2nd edn. Springer, New York (2010)","DOI":"10.1007\/978-1-4419-5945-4"},{"key":"9732_CR21","doi-asserted-by":"crossref","unstructured":"Chi, E., Lange, K.: Splitting methods for convex clustering. J. Comput. Gr. Stat. (in press) (2014)","DOI":"10.1080\/10618600.2014.948181"},{"key":"9732_CR22","unstructured":"Lawson, C.L., Hanson, R.J.: Solving least squares problems. Classics in Applied Mathematics, Society for Industrial Mathematics, new ed., (1987)"},{"issue":"384","key":"9732_CR23","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1080\/01621459.1983.10477029","volume":"78","author":"RL Dykstra","year":"1983","unstructured":"Dykstra, R.L.: An algorithm for restricted least squares regression. J. Am. Stat. Assoc. 78(384), 837\u2013842 (1983)","journal-title":"J. Am. Stat. Assoc."},{"key":"9732_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9298-9","volume-title":"Best Approximation in Inner Product Spaces. CMS Books in Mathematics\/Ouvrages de Math\u00e9matiques de la SMC, 7","author":"F Deutsch","year":"2001","unstructured":"Deutsch, F.: Best Approximation in Inner Product Spaces. CMS Books in Mathematics\/Ouvrages de Math\u00e9matiques de la SMC, 7. Springer, New York (2001)"},{"issue":"1","key":"9732_CR25","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.csda.2006.11.006","volume":"52","author":"MW Berry","year":"2007","unstructured":"Berry, M.W., Browne, M., Langville, A.N., Pauca, V.P., Plemmons, R.J.: Algorithms and applications for approximate nonnegative matrix factorization. Comput. Statist. Data Anal. 52(1), 155\u2013173 (2007)","journal-title":"Comput. Statist. Data Anal."},{"key":"9732_CR26","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1038\/44565","volume":"401","author":"DD Lee","year":"1999","unstructured":"Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788\u2013791 (1999)","journal-title":"Nature"},{"key":"9732_CR27","unstructured":"Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization, in NIPS, pp. 556\u2013562, MIT Press (2001)"},{"issue":"1","key":"9732_CR28","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s11081-007-9001-7","volume":"8","author":"S Boyd","year":"2007","unstructured":"Boyd, S., Kim, S.-J., Vandenberghe, L., Hassibi, A.: A tutorial on geometric programming. Optim. Eng. 8(1), 67\u2013127 (2007)","journal-title":"Optim. Eng."},{"issue":"3","key":"9732_CR29","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1137\/1022058","volume":"22","author":"JG Ecker","year":"1980","unstructured":"Ecker, J.G.: Geometric programming: methods, computations and applications. SIAM Rev. 22(3), 338\u2013362 (1980)","journal-title":"SIAM Rev."},{"key":"9732_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1025-2","volume-title":"The Mathematics of Nonlinear Programming. Undergraduate Texts in Mathematics","author":"AL Peressini","year":"1988","unstructured":"Peressini, A.L., Sullivan, F.E., Uhl Jr, J.J.: The Mathematics of Nonlinear Programming. Undergraduate Texts in Mathematics. Springer, New York (1988)"},{"issue":"1","key":"9732_CR31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/1018001","volume":"18","author":"EL Peterson","year":"1976","unstructured":"Peterson, E.L.: Geometric programming. SIAM Rev. 18(1), 1\u201351 (1976)","journal-title":"SIAM Rev."},{"key":"9732_CR32","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1137\/0116030","volume":"16","author":"U Passy","year":"1968","unstructured":"Passy, U., Wilde, D.J.: A geometric programming algorithm for solving chemical equilibrium problems. SIAM J. Appl. Math. 16, 363\u2013373 (1968)","journal-title":"SIAM J. Appl. Math."},{"key":"9732_CR33","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1287\/opre.1050.0254","volume":"53","author":"SP Boyd","year":"2005","unstructured":"Boyd, S.P., Kim, S.-J., Patil, D.D., Horowitz, M.A.: Digital circuit optimization via geometric programming. Oper. Res. 53, 899\u2013932 (2005)","journal-title":"Oper. Res."},{"issue":"1","key":"9732_CR34","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1093\/biomet\/70.1.257","volume":"70","author":"M Mazumdar","year":"1983","unstructured":"Mazumdar, M., Jefferson, T.R.: Maximum likelihood estimates for multinomial probabilities via geometric programming. Biometrika 70(1), 257\u2013261 (1983)","journal-title":"Biometrika"},{"issue":"3","key":"9732_CR35","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1214\/aop\/1176994422","volume":"9","author":"PD Feigin","year":"1981","unstructured":"Feigin, P.D., Passy, U.: The geometric programming dual to the extinction probability problem in simple branching processes. Ann. Probab. 9(3), 498\u2013503 (1981)","journal-title":"Ann. Probab."},{"key":"9732_CR36","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s10107-012-0612-1","volume":"143","author":"K Lange","year":"2014","unstructured":"Lange, K., Zhou, H.: MM algorithms for geometric and signomial programming. Math. Program.Ser. A 143, 339\u2013356 (2014)","journal-title":"Math. Program.Ser. A"},{"issue":"1","key":"9732_CR37","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1137\/1038003","volume":"38","author":"L Vandenberghe","year":"1996","unstructured":"Vandenberghe, L., Boyd, S.: Semidefinite programming. SIAM Rev. 38(1), 49\u201395 (1996)","journal-title":"SIAM Rev."},{"issue":"1\u20134","key":"9732_CR38","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"LI Rudin","year":"1992","unstructured":"Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenom. 60(1\u20134), 259\u2013268 (1992)","journal-title":"Physica D: Nonlinear Phenom."},{"key":"9732_CR39","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s10851-007-0652-y","volume":"27","author":"T Le","year":"2007","unstructured":"Le, T., Chartrand, R., Asaki, T.J.: A variational approach to reconstructing images corrupted by Poisson noise. J. Math. Imaging Vis 27, 257\u2013263 (2007)","journal-title":"J. Math. Imaging Vis"},{"key":"9732_CR40","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1023\/B:JMIV.0000011320.81911.38","volume":"20","author":"A Chambolle","year":"2004","unstructured":"Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20, 89\u201397 (2004)","journal-title":"J. Math. Imaging Vis."},{"key":"9732_CR41","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1137\/080725891","volume":"2","author":"T Goldstein","year":"2009","unstructured":"Goldstein, T., Osher, S.: The split Bregman method for $$l_1$$ l 1 -regularized problems. SIAM J. Img. Sci. 2, 323\u2013343 (2009)","journal-title":"SIAM J. Img. Sci."},{"key":"9732_CR42","unstructured":"Zhou, H., Armagan, A., Dunson, D.: Path following and empirical Bayes model selection for sparse regressions. arXiv:1201.3528 (2012)"},{"key":"9732_CR43","doi-asserted-by":"crossref","unstructured":"Xiao, W., Wu, Y., Zhou, H.: ConvexLAR: an extension of least angle regression. J. Comput. Gr. Stat. Vol. (in press) (2015)","DOI":"10.1080\/10618600.2014.962700"},{"issue":"4","key":"9732_CR44","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1111\/j.1467-9469.2009.00681.x","volume":"37","author":"H Zhou","year":"2010","unstructured":"Zhou, H., Lange, K.: On the bumpy road to the dominant mode. Scand. J. Stat. 37(4), 612\u2013631 (2010)","journal-title":"Scand. J. Stat."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-015-9732-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-015-9732-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-015-9732-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T22:03:30Z","timestamp":1651269810000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-015-9732-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,18]]},"references-count":44,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,7]]}},"alternative-id":["9732"],"URL":"https:\/\/doi.org\/10.1007\/s10589-015-9732-x","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,18]]}}}