{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T00:53:25Z","timestamp":1774745605163,"version":"3.50.1"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,12,8]],"date-time":"2017-12-08T00:00:00Z","timestamp":1512691200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11322109"],"award-info":[{"award-number":["11322109"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,7]]},"DOI":"10.1007\/s10915-017-0624-3","type":"journal-article","created":{"date-parts":[[2017,12,8]],"date-time":"2017-12-08T09:52:40Z","timestamp":1512726760000},"page":"364-389","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":55,"title":["A Regularized Semi-Smooth Newton Method with Projection Steps for Composite Convex Programs"],"prefix":"10.1007","volume":"76","author":[{"given":"Xiantao","family":"Xiao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongfeng","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1762-0671","authenticated-orcid":false,"given":"Zaiwen","family":"Wen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liwei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,12,8]]},"reference":[{"key":"624_CR1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s11075-012-9653-z","volume":"64","author":"M Ahookhosh","year":"2013","unstructured":"Ahookhosh, M., Amini, K., Bahrami, S.: Two derivative-free projection approaches for systems of large-scale nonlinear monotone equations. Numer. Algorithms 64, 21\u201342 (2013)","journal-title":"Numer. Algorithms"},{"key":"624_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9467-7","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"HH Bauschke","year":"2011","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York (2011)"},{"key":"624_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2011","unstructured":"Boyd, S., Parikh, 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 (2011)","journal-title":"Found. Trends Mach. Learn."},{"key":"624_CR4","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1007\/s10107-015-0965-3","volume":"159","author":"RH Byrd","year":"2016","unstructured":"Byrd, R.H., Chin, G.M., Nocedal, J., Oztoprak, F.: A family of second-order methods for convex \n                        $$\\ell _1$$\n                        \n                            \n                                \n                                    \u2113\n                                    1\n                                \n                            \n                        \n                    -regularized optimization. Math. Program. 159, 435\u2013467 (2016)","journal-title":"Math. Program."},{"key":"624_CR5","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1007\/s10107-014-0853-2","volume":"155","author":"C Chen","year":"2016","unstructured":"Chen, C., Liu, Y.J., Sun, D., Toh, K.C.: A semismooth Newton-CG based dual PPA for matrix spectral norm approximation problems. Math. Program. 155, 435\u2013470 (2016)","journal-title":"Math. Program."},{"key":"624_CR6","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/978-1-4419-9569-8_10","volume-title":"Fixed-Point Algorithms for Inverse Poblems in Science and Engineering, Volume 49 of Springer Optim. Appl.","author":"PL Combettes","year":"2011","unstructured":"Combettes, P.L., Pesquet, J.-C.: Proximal splitting methods in signal processing. In: Bauschke, H.H., Burachik, R., Combettes, P.L., Elser, V., Luke, D.R., Wolkowicz, H. (eds.) Fixed-Point Algorithms for Inverse Poblems in Science and Engineering, Volume 49 of Springer Optim. Appl., pp. 185\u2013212. Springer, New York (2011)"},{"key":"624_CR7","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/978-3-319-41589-5_4","volume-title":"Splitting Methods in Communication, Imaging, Science, and Engineering, Sci. Comput.","author":"D Davis","year":"2016","unstructured":"Davis, D., Yin, W.: Convergence rate analysis of several splitting schemes. In: Glowinski, R., Osher, S.J., Yin, W. (eds.) Splitting Methods in Communication, Imaging, Science, and Engineering, Sci. Comput., pp. 115\u2013163. Springer, Cham (2016)"},{"key":"624_CR8","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1287\/moor.2016.0827","volume":"42","author":"D Davis","year":"2017","unstructured":"Davis, D., Yin, W.: Faster convergence rates of relaxed Peaceman\u2013Rachford and ADMM under regularity assumptions. Math. Oper. Res. 42, 783\u2013805 (2017)","journal-title":"Math. Oper. Res."},{"key":"624_CR9","first-page":"407","volume":"75","author":"T Luca De","year":"1996","unstructured":"De Luca, T., Facchinei, F., Kanzow, C.: A semismooth equation approach to the solution of nonlinear complementarity problems. Math. Program. 75, 407\u2013439 (1996)","journal-title":"Math. Program."},{"key":"624_CR10","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1090\/S0002-9947-1956-0084194-4","volume":"82","author":"J Douglas","year":"1956","unstructured":"Douglas, J., Rachford, H.H.: On the numerical solution of heat conduction problems in two and three space variables. Trans. Am. Math. Soc. 82, 421\u2013439 (1956)","journal-title":"Trans. Am. Math. Soc."},{"key":"624_CR11","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/BF01581204","volume":"55","author":"J Eckstein","year":"1992","unstructured":"Eckstein, J., Bertsekas, D.P.: On the Douglas\u2013Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55, 293\u2013318 (1992)","journal-title":"Math. Program."},{"key":"624_CR12","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems","author":"F Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. II. Springer, New York (2003)"},{"key":"624_CR13","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s00607-004-0083-1","volume":"74","author":"JY Fan","year":"2005","unstructured":"Fan, J.Y., Yuan, Y.X.: On the quadratic convergence of the Levenberg\u2013Marquardt method without nonsingularity assumption. Computing 74, 23\u201339 (2005)","journal-title":"Computing"},{"key":"624_CR14","doi-asserted-by":"crossref","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, 17\u201340 (1976)","journal-title":"Comput. Math. Appl."},{"key":"624_CR15","first-page":"41","volume":"9","author":"R Glowinski","year":"1975","unstructured":"Glowinski, R., Marrocco, A.: Sur l\u2019approximation, par \u00e9l\u00e9ments finis d\u2019ordre un, et la r\u00e9solution, par p\u00e9nalisation-dualit\u00e9, d\u2019une classe de probl\u00e8mes de Dirichlet non lin\u00e9aires. Rev. Fran\u00e7aise Automat. Informat. Recherche Op\u00e9rationnelle S\u00e9r. Rouge Anal. Num\u00e9r. 9, 41\u201376 (1975)","journal-title":"Rev. Fran\u00e7aise Automat. Informat. Recherche Op\u00e9rationnelle S\u00e9r. Rouge Anal. Num\u00e9r."},{"key":"624_CR16","doi-asserted-by":"crossref","first-page":"035007","DOI":"10.1088\/0266-5611\/24\/3\/035007","volume":"24","author":"R Griesse","year":"2008","unstructured":"Griesse, R., Lorenz, D.A.: A semismooth Newton method for Tikhonov functionals with sparsity constraints. Inverse Probl. 24, 035007 (2008)","journal-title":"Inverse Probl."},{"key":"624_CR17","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1006\/jmaa.1995.1412","volume":"196","author":"H Jiang","year":"1995","unstructured":"Jiang, H., Qi, L.: Local uniqueness and convergence of iterative methods for nonsmooth variational inequalities. J. Math. Anal. Appl. 196, 314\u2013331 (1995)","journal-title":"J. Math. Anal. Appl."},{"key":"624_CR18","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1137\/130921428","volume":"24","author":"JD Lee","year":"2014","unstructured":"Lee, J.D., Sun, Y., Saunders, M.A.: Proximal Newton-type methods for minimizing composite functions. SIAM J. Optim. 24, 1420\u20131443 (2014)","journal-title":"SIAM J. Optim."},{"key":"624_CR19","doi-asserted-by":"crossref","first-page":"1625","DOI":"10.1093\/imanum\/drq015","volume":"31","author":"Q Li","year":"2011","unstructured":"Li, Q., Li, D.H.: A class of derivative-free methods for large-scale nonlinear monotone equations. IMA J. Numer. Anal. 31, 1625\u20131635 (2011)","journal-title":"IMA J. Numer. Anal."},{"key":"624_CR20","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1137\/0716071","volume":"16","author":"P-L Lions","year":"1979","unstructured":"Lions, P.-L., Mercier, B.: Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16, 964\u2013979 (1979)","journal-title":"SIAM J. Numer. Anal."},{"key":"624_CR21","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1137\/0315061","volume":"15","author":"R Mifflin","year":"1977","unstructured":"Mifflin, R.: Semismooth and semiconvex functions in constrained optimization. SIAM J. Control Optim. 15, 959\u2013972 (1977)","journal-title":"SIAM J. Control Optim."},{"key":"624_CR22","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1137\/120892167","volume":"24","author":"A Milzarek","year":"2014","unstructured":"Milzarek, A., Ulbrich, M.: A semismooth Newton method with multidimensional filter globalization for \n                        $$l_1$$\n                        \n                            \n                                \n                                    l\n                                    1\n                                \n                            \n                        \n                    -optimization. SIAM J. Optim. 24, 298\u2013333 (2014)","journal-title":"SIAM J. Optim."},{"key":"624_CR23","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":"624_CR24","volume-title":"Iterative Solution of Nonlinear Equations in Several Variables","author":"JM Ortega","year":"1970","unstructured":"Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970)"},{"key":"624_CR25","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1137\/0803021","volume":"3","author":"J-S Pang","year":"1993","unstructured":"Pang, J.-S., Qi, L.Q.: Nonsmooth equations: motivation and algorithms. SIAM J. Optim. 3, 443\u2013465 (1993)","journal-title":"SIAM J. Optim."},{"key":"624_CR26","unstructured":"Patrinos, P., Stella, L., Bemporad, A..: Forward\u2013backward truncated Newton methods for convex composite optimization. \n                        http:\/\/arxiv.org\/abs\/1402.6655\n                        \n                    , 02 (2014)"},{"key":"624_CR27","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1287\/moor.18.1.227","volume":"18","author":"LQ Qi","year":"1993","unstructured":"Qi, L.Q.: Convergence analysis of some algorithms for solving nonsmooth equations. Math. Oper. Res. 18, 227\u2013244 (1993)","journal-title":"Math. Oper. Res."},{"key":"624_CR28","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/BF01581275","volume":"58","author":"LQ Qi","year":"1993","unstructured":"Qi, L.Q., Sun, J.: A nonsmooth version of Newton\u2019s method. Math. Program. 58, 353\u2013367 (1993)","journal-title":"Math. Program."},{"key":"624_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational Analysis","author":"RT Rockafellar","year":"1998","unstructured":"Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin (1998)"},{"key":"624_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-4340-7","volume-title":"Introduction to Piecewise Differentiable Equations, Springer Briefs in Optimization","author":"S Scholtes","year":"2012","unstructured":"Scholtes, S.: Introduction to Piecewise Differentiable Equations, Springer Briefs in Optimization. Springer, New York (2012)"},{"key":"624_CR31","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF02190320","volume":"81","author":"A Shapiro","year":"1994","unstructured":"Shapiro, A.: Directionally nondifferentiable metric projection. J. Optim. Theory Appl. 81, 203\u2013204 (1994)","journal-title":"J. Optim. Theory Appl."},{"key":"624_CR32","first-page":"355","volume-title":"Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods (Lausanne, 1997)","author":"MV Solodov","year":"1999","unstructured":"Solodov, M.V., Svaiter, B.F.: A globally convergent inexact Newton method for systems of monotone equations. In: Fukushima, M., Qi, L. (eds.) Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods (Lausanne, 1997), vol. 22, pp. 355\u2013369. Kluwer Academic Publishers, Dordrecht (1999)"},{"key":"624_CR33","first-page":"59","volume":"6","author":"MV Solodov","year":"1999","unstructured":"Solodov, M.V., Svaiter, B.F.: A hybrid projection-proximal point algorithm. J. Convex Anal. 6, 59\u201370 (1999)","journal-title":"J. Convex Anal."},{"key":"624_CR34","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1137\/S1052623494274970","volume":"7","author":"D Sun","year":"1997","unstructured":"Sun, D., Han, J.: Newton and quasi-Newton methods for a class of nonsmooth equations and related problems. SIAM J. Optim. 7, 463\u2013480 (1997)","journal-title":"SIAM J. Optim."},{"key":"624_CR35","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1287\/moor.27.1.150.342","volume":"27","author":"D Sun","year":"2002","unstructured":"Sun, D., Sun, J.: Semismooth matrix-valued functions. Math. Oper. Res. 27, 150\u2013169 (2002)","journal-title":"Math. Oper. Res."},{"key":"624_CR36","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":"624_CR37","volume-title":"Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function spaces, Society for Industrial and Applied Mathematics SIAM), Philadelphia, PA","author":"M Ulbrich","year":"2011","unstructured":"Ulbrich, M.: Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function spaces, Society for Industrial and Applied Mathematics SIAM), Philadelphia, PA. Mathematical Optimization Society, Philadelphia (2011)"},{"key":"624_CR38","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1137\/080714488","volume":"31","author":"E Berg van den","year":"2008","unstructured":"van den Berg, E., Friedlander, M.P.: Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31, 890\u2013912 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"624_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":"624_CR40","doi-asserted-by":"crossref","first-page":"2479","DOI":"10.1109\/TSP.2009.2016892","volume":"57","author":"SJ Wright","year":"2009","unstructured":"Wright, S.J., Nowak, R.D., Figueiredo, M.A.T.: Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57, 2479\u20132493 (2009)","journal-title":"IEEE Trans. Signal Process."},{"key":"624_CR41","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/S0377-0427(02)00730-6","volume":"152","author":"N Xiu","year":"2003","unstructured":"Xiu, N., Zhang, J.: Some recent advances in projection-type methods for variational inequalities. J. Comput. Appl. Math. 152, 559\u2013585 (2003)","journal-title":"J. Comput. Appl. Math."},{"key":"624_CR42","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 \n                        $$\\ell _{1}$$\n                        \n                            \n                                \n                                    \u2113\n                                    1\n                                \n                            \n                        \n                    -problems in compressive sensing. SIAM J. Sci. Comput. 33, 250\u2013278 (2011)","journal-title":"SIAM J. Sci. Comput."},{"key":"624_CR43","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1137\/080718206","volume":"20","author":"XY Zhao","year":"2010","unstructured":"Zhao, X.Y., Sun, D., Toh, K.C.: A Newton-CG augmented Lagrangian method for semidefinite programming. SIAM J. Optim. 20, 1737\u20131765 (2010)","journal-title":"SIAM J. Optim."},{"key":"624_CR44","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1137\/S1052623499357957","volume":"11","author":"Y-B Zhao","year":"2001","unstructured":"Zhao, Y.-B., Li, D.: Monotonicity of fixed point and normal mappings associated with variational inequality and its application. SIAM J. Optim. 11, 962\u2013973 (2001)","journal-title":"SIAM J. Optim."},{"key":"624_CR45","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s10957-004-1721-7","volume":"125","author":"G Zhou","year":"2005","unstructured":"Zhou, G., Toh, K.C.: Superlinear convergence of a Newton-type algorithm for monotone equations. J. Optim. Theory Appl. 125, 205\u2013221 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"624_CR46","doi-asserted-by":"crossref","first-page":"2231","DOI":"10.1090\/S0025-5718-08-02121-2","volume":"77","author":"WJ Zhou","year":"2008","unstructured":"Zhou, W.J., Li, D.H.: A globally convergent BFGS method for nonlinear monotone equations without any merit functions. Math. Comput. 77, 2231\u20132240 (2008)","journal-title":"Math. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0624-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0624-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0624-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,6,7]],"date-time":"2018-06-07T10:02:26Z","timestamp":1528365746000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0624-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,8]]},"references-count":46,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,7]]}},"alternative-id":["624"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0624-3","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,8]]}}}