{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T06:01:14Z","timestamp":1775628074757,"version":"3.50.1"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T00:00:00Z","timestamp":1625788800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T00:00:00Z","timestamp":1625788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1007\/s10208-021-09528-6","type":"journal-article","created":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T19:03:46Z","timestamp":1625857426000},"page":"1171-1217","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["Kurdyka\u2013\u0141ojasiewicz Exponent via Inf-projection"],"prefix":"10.1007","volume":"22","author":[{"given":"Peiran","family":"Yu","sequence":"first","affiliation":[]},{"given":"Guoyin","family":"Li","sequence":"additional","affiliation":[]},{"given":"Ting Kei","family":"Pong","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,9]]},"reference":[{"key":"9528_CR1","doi-asserted-by":"publisher","first-page":"1637","DOI":"10.1137\/16M1084754","volume":"27","author":"M Ahn","year":"2017","unstructured":"M. Ahn, J. S. Pang and J. Xin, Difference-of-convex learning: directional stationarity, optimality, and sparsity, SIAM J. Optim. 27 (2017), 1637\u20131665.","journal-title":"SIAM J. Optim."},{"key":"9528_CR2","doi-asserted-by":"crossref","unstructured":"C. M. Ala\u00edz, \u00c1. Barbero J. R. Dorronsoro, Group fused lasso, in Artificial Neural Networks and Machine Learning\u2013ICANN 2013. Lecture Notes in Computer Science, vol 8131. (V. Mladenov, P. Koprinkova-Hristova, G. Palm, A. E. P. Villa, B. Appollini, N. Kasabov, eds) Springer, Berlin, Heidelberg, (2013), pp. 66\u201373.","DOI":"10.1007\/978-3-642-40728-4_9"},{"key":"9528_CR3","first-page":"365","volume":"15","author":"F. J. Arag\u00f3n Artacho","year":"2008","unstructured":"F. J. Arag\u00f3n Artacho and M. H. Geoffroy, Characterization of metric regularity of subdifferentials, J. Convex Anal. 15 (2008), 365\u2013380.","journal-title":"J. Convex Anal"},{"key":"9528_CR4","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10107-007-0133-5","volume":"116","author":"H Attouch","year":"2009","unstructured":"H. Attouch and J. Bolte, On the convergence of the proximal algorithm for nonsmooth functions involving analytic features, Math. Program. 116 (2009), 5\u201316.","journal-title":"Math. Program."},{"key":"9528_CR5","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1287\/moor.1100.0449","volume":"35","author":"H Attouch","year":"2010","unstructured":"H. Attouch, J. Bolte, P. Redont and A. Soubeyran, Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-\u0141ojasiewicz inequality, Math. Oper. Res. 35 (2010), 438\u2013457.","journal-title":"Math. Oper. Res."},{"key":"9528_CR6","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s10107-011-0484-9","volume":"137","author":"H Attouch","year":"2013","unstructured":"H. Attouch, J. Bolte and B. F. Svaiter, Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods, Math. Program. 137 (2013), 91\u2013129.","journal-title":"Math. Program."},{"key":"9528_CR7","unstructured":"A. Auslender and M. Teboulle, Asymptotic Cones and Functions in Optimization and Variational Inequalities, Springer, 2003."},{"key":"9528_CR8","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1137\/S0036144593251710","volume":"38","author":"HH Bauschke","year":"1996","unstructured":"H. H. Bauschke and J. M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Review 38 (1996), 367\u2013426.","journal-title":"SIAM Review"},{"key":"9528_CR9","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s101070050083","volume":"86","author":"HH Bauschke","year":"1999","unstructured":"H. H. Bauschke, J. M. Borwein and W. Li, Strong conical hull intersection property, bounded linear regularity, Jameson\u2019s property (G), and error bounds in convex optimization, Math. Program. 86 (1999), 135\u2013160.","journal-title":"Math. Program."},{"key":"9528_CR10","first-page":"401","volume":"2","author":"HH Bauschke","year":"2006","unstructured":"H. H. Bauschke, P. L. Combettes and D. Noll, Joint minimization with alternating Bregman proximity operators, Pac. J. Optim. 2 (2006), 401\u2013424.","journal-title":"Pac. J. Optim."},{"key":"9528_CR11","doi-asserted-by":"crossref","unstructured":"A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MPS-SIAM Series on Optimization, (2001).","DOI":"10.1137\/1.9780898718829"},{"key":"9528_CR12","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1137\/050644641","volume":"17","author":"J Bolte","year":"2007","unstructured":"J. Bolte, A. Daniilidis and A. Lewis, The \u0141ojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems, SIAM J. Optim. 17 (2007), 1205\u20131223.","journal-title":"SIAM J. Optim."},{"key":"9528_CR13","doi-asserted-by":"publisher","first-page":"556","DOI":"10.1137\/060670080","volume":"18","author":"J Bolte","year":"2007","unstructured":"J. Bolte, A. Daniilidis, A. Lewis and M. Shiota, Clarke subgradients of stratifiable functions, SIAM J. Optim. 18 (2007), 556\u2013572.","journal-title":"SIAM J. Optim."},{"key":"9528_CR14","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1007\/s10107-016-1091-6","volume":"165","author":"J Bolte","year":"2017","unstructured":"J. Bolte, T. P. Nguyen, J. Peypouquet and B. W. Suter, From error bounds to the complexity of first-order descent methods for convex functions, Math. Program. 165 (2017), 471\u2013507.","journal-title":"Math. Program."},{"key":"9528_CR15","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s10107-013-0701-9","volume":"146","author":"J Bolte","year":"2014","unstructured":"J. Bolte, S. Sabach and M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Math. Program. 146 (2014), 459\u2013494.","journal-title":"Math. Program."},{"key":"9528_CR16","doi-asserted-by":"crossref","unstructured":"J. Borwein and A. Lewis, Convex Analysis and Nonlinear Optimization, 2nd edition, Springer, 2006.","DOI":"10.1007\/978-0-387-31256-9"},{"key":"9528_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2010","unstructured":"S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Found. Trend. in Mach. Learn. 3 (2010), 1\u2013122.","journal-title":"Found. Trend. in Mach. Learn."},{"key":"9528_CR18","doi-asserted-by":"publisher","first-page":"2332","DOI":"10.1137\/17M1116325","volume":"27","author":"Y Cui","year":"2017","unstructured":"Y. Cui, C. Ding and X. Zhao, Quadratic growth conditions for convex matrix optimization problems associated with spectral functions, SIAM J. Optim. 27 (2017), 2332\u20132355.","journal-title":"SIAM J. Optim."},{"key":"9528_CR19","unstructured":"Y. Cui, D. F. Sun and K. C. Toh, On the asymptotic superlinear convergence of the augmented Lagrangian method for semidefinite programming with multiple solutions, Preprint (2016). Available at https:\/\/arxiv.org\/abs\/1610.00875."},{"key":"9528_CR20","doi-asserted-by":"publisher","first-page":"51","DOI":"10.4064\/ap87-0-5","volume":"87","author":"D D\u2019Acunto","year":"2005","unstructured":"D. D\u2019Acunto and K. Kurdyka, Explicit bounds for the \u0141ojasiewicz exponent in the gradient inequality for polynomials, Ann. Polon. Math. 87 (2005), 51\u201361.","journal-title":"Ann. Polon. Math."},{"key":"9528_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-87821-8","volume-title":"Implicit Functions and Solution Mappings","author":"AL Dontchev","year":"2009","unstructured":"A. L. Dontchev and R. T. Rockafellar, Implicit Functions and Solution Mappings, Springer, New York, 2009."},{"key":"9528_CR22","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/s10107-019-01432-w","volume":"185","author":"D Drusvyatskiy","year":"2021","unstructured":"D. Drusvyatskiy, A. D. Ioffe and A. S. Lewis, Nonsmooth optimization using Taylor-like models: error bounds, convergence, and termination criteria, Math. Program. 185 (2021), 357-383.","journal-title":"Math. Program."},{"key":"9528_CR23","doi-asserted-by":"publisher","first-page":"919","DOI":"10.1287\/moor.2017.0889","volume":"43","author":"D Drusvyatskiy","year":"2018","unstructured":"D. Drusvyatskiy and A. Lewis, Error bounds, quadratic growth, and linear convergence of proximal methods, Math. Oper. Res. 43 (2018), 919\u2013948.","journal-title":"Math. Oper. Res."},{"key":"9528_CR24","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1007\/s10107-016-1048-9","volume":"162","author":"D Drusvyatskiy","year":"2017","unstructured":"D. Drusvyatskiy, G. Li and H. Wolkowicz, A note on alternating projections for ill-posed semidefinite feasibility problems, Math. Program. 162 (2017), 537\u2013548.","journal-title":"Math. Program."},{"key":"9528_CR25","doi-asserted-by":"crossref","unstructured":"J. Fan, Comments on \u201cwavelets in statistics: a review\u201d by A. Antoniadis, J. Ital. Stat. Soc. 6 (1997), 131\u2013138.","DOI":"10.1007\/BF03178906"},{"key":"9528_CR26","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems","author":"F Fachinei","year":"2003","unstructured":"F. Fachinei and J.-S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer, New York, 2003."},{"key":"9528_CR27","doi-asserted-by":"publisher","first-page":"874","DOI":"10.1007\/s10957-014-0642-3","volume":"165","author":"P Frankel","year":"2015","unstructured":"P. Frankel, G. Garrigos and J. Peypouquet, Splitting methods with variable metric for Kurdyka-\u0141ojasiewicz functions and general convergence rates, J. Optim. Theory Appl. 165 (2015), 874\u2013900.","journal-title":"J. Optim. Theory Appl."},{"key":"9528_CR28","doi-asserted-by":"publisher","first-page":"1999","DOI":"10.1137\/130940785","volume":"24","author":"MP Friedlander","year":"2014","unstructured":"M. P. Friedlander, I. Mac\u00eado and T. K. Pong, Gauge optimization and duality, SIAM J. Optim. 24 (2014), 1999\u20132022.","journal-title":"SIAM J. Optim."},{"key":"9528_CR29","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s10107-008-0240-y","volume":"122","author":"JW Helton","year":"2010","unstructured":"J. W. Helton and J. Nie, Semidefinite representation of convex sets, Math. Program. 122 (2010), 21\u201364.","journal-title":"Math. Program."},{"key":"9528_CR30","doi-asserted-by":"publisher","first-page":"1603","DOI":"10.1137\/18M1174313","volume":"29","author":"R Jiang","year":"2019","unstructured":"R. Jiang and D. Li, Novel reformulations and efficient algorithms for the generalized trust region subproblem, SIAM J. Optim. 29 (2019), 1603\u20131633.","journal-title":"SIAM J. Optim."},{"key":"9528_CR31","doi-asserted-by":"publisher","first-page":"769","DOI":"10.5802\/aif.1638","volume":"48","author":"K Kurdyka","year":"1998","unstructured":"K. Kurdyka, On gradients of functions definable in o-minimal structures, Ann. Inst. Fourier 48 (1998) 769\u2013783.","journal-title":"Ann. Inst. Fourier"},{"key":"9528_CR32","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s10107-014-0806-9","volume":"153","author":"G Li","year":"2015","unstructured":"G. Li, B. S. Mordukhovich and T. S. Pham, New fractional error bounds for polynomial systems with applications to H\u00f6lderian stability in optimization and spectral theory of tensors, Math. Program. 153 (2015), 333\u2013362.","journal-title":"Math. Program."},{"key":"9528_CR33","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/s10107-015-0963-5","volume":"159","author":"G Li","year":"2016","unstructured":"G. Li and T. K. Pong, Douglas-Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems, Math. Program. 159 (2016), 371\u2013401.","journal-title":"Math. Program."},{"key":"9528_CR34","doi-asserted-by":"publisher","first-page":"1199","DOI":"10.1007\/s10208-017-9366-8","volume":"18","author":"G Li","year":"2018","unstructured":"G. Li and T. K. Pong, Calculus of the exponent of Kurdyka-\u0141ojasiewicz inequality and its applications to linear convergence of first-order methods, Found. Comput. Math. 18 (2018), 1199\u20131232.","journal-title":"Found. Comput. Math."},{"key":"9528_CR35","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/s10589-017-9900-2","volume":"67","author":"T Liu","year":"2017","unstructured":"T. Liu and T. K. Pong, Further properties of the forward-backward envelope with applications to difference-of-convex programming, Comput. Optim. Appl. 67 (2017), 489\u2013520.","journal-title":"Comput. Optim. Appl."},{"key":"9528_CR36","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s10589-019-00067-z","volume":"73","author":"T Liu","year":"2019","unstructured":"T. Liu, T. K. Pong and A. Takeda, A refined convergence analysis of pDCA$$_e$$ with applications to simultaneous sparse recovery and outlier detection, Comput. Optim. Appl. 73 (2019), 69\u2013100.","journal-title":"Comput. Optim. Appl."},{"key":"9528_CR37","unstructured":"H. Liu, W. Wu and A. M.-C. So, Quadratic optimization with orthogonality constraints: explicit \u0141ojasiewicz exponent and linear convergence of line-search methods, ICML, (2016), pp. 1158\u20131167."},{"key":"9528_CR38","first-page":"87","volume-title":"Une propri\u00e9t\u00e9 topologique des sous-ensembles analytiques r\u00e9els, in Les \u00c9quations aux D\u00e9riv\u00e9es Partielles","author":"S \u0141ojasiewicz","year":"1963","unstructured":"S. \u0141ojasiewicz, Une propri\u00e9t\u00e9 topologique des sous-ensembles analytiques r\u00e9els, in Les \u00c9quations aux D\u00e9riv\u00e9es Partielles, \u00c9ditions du Centre National de la Recherche Scientifique, Paris, 1963, pp. 87\u201389."},{"key":"9528_CR39","doi-asserted-by":"publisher","first-page":"2304","DOI":"10.1137\/15M1051634","volume":"28","author":"BF Louren\u00e7o","year":"2018","unstructured":"B. F. Louren\u00e7o, M. Muramatsu and T. Tsuchiya, Facial reduction and partial polyhedrality, SIAM J. Optim. 28 (2018), 2304\u20132326.","journal-title":"SIAM J. Optim."},{"key":"9528_CR40","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511983658","volume-title":"Mathematical Programs with Equilibrium Constraints","author":"ZQ Luo","year":"1996","unstructured":"Z. Q. Luo, J. S. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints, Cambridge University Press, Cambridge, 1996."},{"key":"9528_CR41","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/BF02096261","volume":"46","author":"ZQ Luo","year":"1993","unstructured":"Z. Q. Luo and P. Tseng, Error bounds and convergence analysis of feasible descent methods: a general approach, Ann. Oper. Res. 46 (1993), 157\u2013178.","journal-title":"Ann. Oper. Res."},{"key":"9528_CR42","first-page":"123","volume":"1","author":"N Parikh","year":"2013","unstructured":"N. Parikh and S. P. Boyd, Proximal algorithms, Found. Trends Optimiz. 1 (2013), 123\u2013231.","journal-title":"Found. Trends Optimiz."},{"key":"9528_CR43","doi-asserted-by":"crossref","unstructured":"G. Pataki, The geometry of semidefinite programming, in Handbook of semidefinite programming (H. Wolkowicz, R. Saigal, and L. Vandenberghe, eds.), Kluwer Acad. Publ., Boston, MA, (2000), pp. 29\u201365.","DOI":"10.1007\/978-1-4615-4381-7_3"},{"key":"9528_CR44","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1137\/070697835","volume":"52","author":"B Recht","year":"2010","unstructured":"B. Recht, M. Fazel and P. Parrilo, Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization, SIAM Review 52 (2010), 471\u2013501.","journal-title":"SIAM Review"},{"key":"9528_CR45","doi-asserted-by":"crossref","unstructured":"R. T. Rockafellar, Convex Analysis, Princeton University Press, 1970.","DOI":"10.1515\/9781400873173"},{"key":"9528_CR46","doi-asserted-by":"crossref","unstructured":"R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, Springer, 1998.","DOI":"10.1007\/978-3-642-02431-3"},{"key":"9528_CR47","doi-asserted-by":"publisher","first-page":"2554","DOI":"10.1023\/A:1022940300114","volume":"115","author":"A Shapiro","year":"2003","unstructured":"A. Shapiro, Sensitivity analysis of generalized equations, J. Math. Sci. 115 (2003), 2554\u20132565.","journal-title":"J. Math. Sci."},{"key":"9528_CR48","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/978-1-4615-4381-7_4","volume-title":"Duality and optimality conditions, in Handbook of semidefinite programming","author":"A Shapiro","year":"2000","unstructured":"A. Shapiro and K. Scheinberg, Duality and optimality conditions, in Handbook of semidefinite programming, Kluwer Acad. Publ., Boston, MA, 2000, pp. 67\u2013110."},{"key":"9528_CR49","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1007\/s10589-017-9912-y","volume":"67","author":"L Stella","year":"2017","unstructured":"L. Stella, A. Themelis and P. Patrinos, Forward-backward quasi-Newton methods for nonsmooth optimization problems, Comput. Optim. Appl. 67 (2017), 443\u2013487.","journal-title":"Comput. Optim. Appl."},{"key":"9528_CR50","doi-asserted-by":"publisher","first-page":"1228","DOI":"10.1137\/S1052623498338606","volume":"10","author":"JF Sturm","year":"2000","unstructured":"J. F. Sturm, Error bounds for linear matrix inequalities, SIAM J. Optim. 10 (2000), 1228\u20131248.","journal-title":"SIAM J. Optim."},{"key":"9528_CR51","doi-asserted-by":"crossref","unstructured":"H. Tuy, Convex Analysis and Global Optimization, Springer, 2nd edition, (2016).","DOI":"10.1007\/978-3-319-31484-6"},{"key":"9528_CR52","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1007\/s10589-012-9480-0","volume":"53","author":"L Tun\u00e7el","year":"2012","unstructured":"L. Tun\u00e7el and H. Wolkowicz, Strong duality and minimal representations for cone optimization, Comput. Optim. Appl. 53 (2012), 619\u2013648.","journal-title":"Comput. Optim. Appl."},{"key":"9528_CR53","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/s10107-007-0170-0","volume":"117","author":"P Tseng","year":"2009","unstructured":"P. Tseng and S. Yun, A coordinate gradient descent method for nonsmooth separable minimization, Math. Program. 117 (2009), 387\u2013423.","journal-title":"Math. Program."},{"key":"9528_CR54","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000055","volume":"9","author":"M Udell","year":"2016","unstructured":"M. Udell, C. Horn, R. Zadeh and S. Boyd, Generalized low rank models, Found. Trends in Mach. Learn. 9 (2016), 1\u2013118.","journal-title":"Found. Trends in Mach. Learn."},{"key":"9528_CR55","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/0024-3795(92)90407-2","volume":"170","author":"A Watson","year":"1992","unstructured":"A. Watson, Characterization of the subdifferential of some matrix norms, Linear Algebra Appl. 170 (1992), 33\u201345.","journal-title":"Linear Algebra Appl."},{"key":"9528_CR56","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s10589-017-9954-1","volume":"69","author":"B Wen","year":"2018","unstructured":"B. Wen, X. Chen and T. K. Pong, A proximal difference-of-convex algorithm with extrapolation, Comput. Optim. Appl. 69 (2018), 297\u2013324.","journal-title":"Comput. Optim. Appl."},{"key":"9528_CR57","doi-asserted-by":"publisher","first-page":"A536","DOI":"10.1137\/140952363","volume":"37","author":"P Yin","year":"2015","unstructured":"P. Yin, Y. Lou, Q. He and J. Xin, Minimization of $$\\ell _{1-2}$$ for compressed sensing, SIAM J. Sci. Comput. 37 (2015), A536\u2013A563.","journal-title":"SIAM J. Sci. Comput."},{"key":"9528_CR58","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/s10107-018-1280-6","volume":"174","author":"M Yue","year":"2019","unstructured":"M. Yue, Z. Zhou and A. M.-C. So, A family of inexact SQA methods for non-smooth convex minimization with provable convergence guarantees based on the Luo-Tseng error bound property, Math. Program. 174 (2019), 327\u2013358.","journal-title":"Math. Program."},{"key":"9528_CR59","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1214\/09-AOS729","volume":"38","author":"C-H Zhang","year":"2010","unstructured":"C.-H. Zhang, Nearly unbiased variable selection under minimax concave penalty, Ann. Stat. 38 (2010), 894\u2013942.","journal-title":"Ann. Stat."},{"key":"9528_CR60","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1007\/s10107-016-1100-9","volume":"165","author":"Z Zhou","year":"2017","unstructured":"Z. Zhou and A. M.-C. So, A unified approach to error bounds for structured convex optimization problems, Math. Program. 165 (2017), 689\u2013728.","journal-title":"Math. Program."}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-021-09528-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10208-021-09528-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-021-09528-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,5]],"date-time":"2023-02-05T00:09:16Z","timestamp":1675555756000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10208-021-09528-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,9]]},"references-count":60,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["9528"],"URL":"https:\/\/doi.org\/10.1007\/s10208-021-09528-6","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,9]]},"assertion":[{"value":"8 February 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 January 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 June 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 July 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}