{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T04:32:35Z","timestamp":1771475555567,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2013,12,29]],"date-time":"2013-12-29T00:00:00Z","timestamp":1388275200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2015,2]]},"DOI":"10.1007\/s10107-013-0737-x","type":"journal-article","created":{"date-parts":[[2013,12,28]],"date-time":"2013-12-28T15:54:07Z","timestamp":1388246047000},"page":"1-45","source":"Crossref","is-referenced-by-count":53,"title":["Bundle-level type methods uniformly optimal for smooth and nonsmooth convex optimization"],"prefix":"10.1007","volume":"149","author":[{"given":"Guanghui","family":"Lan","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,12,29]]},"reference":[{"key":"737_CR1","unstructured":"Ahmed, S.: Smooth Minimization of Two-Stage Stochastic Linear Programs. Manuscript, Georgia Institute of Technology (2006)"},{"key":"737_CR2","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1137\/S1052623403427823","volume":"16","author":"A Auslender","year":"2006","unstructured":"Auslender, A., Teboulle, M.: Interior gradient and proximal methods for convex and conic optimization. SIAM J. Optim. 16, 697\u2013725 (2006)","journal-title":"SIAM J. Optim."},{"key":"737_CR3","unstructured":"Becker, S., Bobin, J., Cand\u00e8s, E.: NESTA: A Fast and Accurate First-Order Method for Sparse Recovery. Manuscript, California Institute of Technology (2009)"},{"key":"737_CR4","doi-asserted-by":"crossref","unstructured":"Ben-Tal, A., Nemirovski, A.S.: Lectures on Modern Convex Optimization: Analysis, Algorithms. Engineering Applications. MPS-SIAM Series on Optimization. SIAM, Philadelphia (2000)","DOI":"10.1137\/1.9780898718829"},{"key":"737_CR5","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/s10107-004-0553-4","volume":"102","author":"A Ben-Tal","year":"2005","unstructured":"Ben-Tal, A., Nemirovski, A.S.: Non-euclidean restricted memory level method for large-scale convex optimization. Math. Program. 102, 407\u2013456 (2005)","journal-title":"Math. Program."},{"key":"737_CR6","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/BF01386389","volume":"1","author":"EW Chenny","year":"1959","unstructured":"Chenny, E.W., Goldstein, A.A.: Newton\u2019s methods for convex programming and tchebytcheff approximation. Numer. Math. 1, 253\u2013268 (1959)","journal-title":"Numer. Math."},{"key":"737_CR7","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1137\/060670985","volume":"30","author":"A d\u2019Aspremont","year":"2008","unstructured":"d\u2019Aspremont, A., Banerjee, O., El Ghaoui, L.: First-order methods for sparse covariance selection. SIAM J. Matrix Anal. Appl. 30, 56\u201366 (2008)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"737_CR8","unstructured":"Devolder, O., Glineur, F., Nesterov, Y.E.: First-Order Methods of Smooth Convex Optimization with Inexact Oracle. Manuscript, CORE, Universit\u00e9 catholique de Louvain, Louvain-la-Neuve, Belgium (Dec 2010)"},{"key":"737_CR9","unstructured":"Ghadimi, S., Lan, G.: Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization, II: shrinking procedures and optimal algorithms. Technical report, SIAM J. Optim. (to appear) (2010)"},{"key":"737_CR10","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1137\/110848864","volume":"22","author":"S Ghadimi","year":"2012","unstructured":"Ghadimi, S., Lan, G.: Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization, I: a generic algorithmic framework. SIAM J. Optim. 22, 1469\u20131492 (2012)","journal-title":"SIAM J. Optim."},{"key":"737_CR11","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1137\/S1052623497328987","volume":"10","author":"C Helmberg","year":"2000","unstructured":"Helmberg, C., Rendl, F.: A spectral bundle method for semidefinite programming. SIAM J. Optim. 10, 673\u2013696 (2000)","journal-title":"SIAM J. Optim."},{"key":"737_CR12","doi-asserted-by":"crossref","first-page":"263","DOI":"10.6028\/jres.049.027","volume":"49","author":"A Hoffman","year":"1952","unstructured":"Hoffman, A.: On approximate solutions of systems of linear inequalities. J. Res. Natl. Bureau Stand Sect. B Math. Sci. 49, 263\u2013265 (1952)","journal-title":"J. Res. Natl. Bureau Stand Sect. B Math. Sci."},{"key":"737_CR13","unstructured":"Juditsky, A., Nemirovski, A.S., Tauvel, C.: Solving Variational Inequalities with Stochastic Mirror-Prox Algorithm. Manuscript, Georgia Institute of Technology, Atlanta, GA (2008)"},{"key":"737_CR14","first-page":"703","volume":"8","author":"JE Kelley","year":"1960","unstructured":"Kelley, J.E.: The cutting plane method for solving convex programs. J. SIAM 8, 703\u2013712 (1960)","journal-title":"J. SIAM"},{"key":"737_CR15","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1007\/BF02591907","volume":"27","author":"KC Kiwiel","year":"1983","unstructured":"Kiwiel, K.C.: An aggregate subgradient method for nonsmooth convex minimization. Math. Program. 27, 320\u2013341 (1983)","journal-title":"Math. Program."},{"key":"737_CR16","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF01585731","volume":"46","author":"KC Kiwiel","year":"1990","unstructured":"Kiwiel, K.C.: Proximity control in bundle methods for convex nondifferentiable minimization. Math. Program. 46, 105\u2013122 (1990)","journal-title":"Math. Program."},{"key":"737_CR17","first-page":"89","volume":"69","author":"KC Kiwiel","year":"1995","unstructured":"Kiwiel, K.C.: Proximal level bundle method for convex nondifferentable optimization, saddle point problems and variational inequalities. Math. Program. Ser. B 69, 89\u2013109 (1995)","journal-title":"Math. Program. Ser. B"},{"key":"737_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10107-008-0261-6","volume":"126","author":"G Lan","year":"2011","unstructured":"Lan, G., Lu, Z., Monteiro, R.D.C.: Primal-dual first-order methods with $${\\cal O}(1\/\\epsilon )$$ O ( 1 \/ \u03f5 ) iteration-complexity for cone programming. Math. Program. 126, 1\u201329 (2011)","journal-title":"Math. Program."},{"issue":"1","key":"737_CR19","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/s10107-010-0434-y","volume":"133","author":"G Lan","year":"2012","unstructured":"Lan, G.: An optimal method for stochastic composite optimization. Math. Program. 133(1), 365\u2013397 (2012)","journal-title":"Math. Program."},{"key":"737_CR20","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/s10107-011-0442-6","volume":"134","author":"G Lan","year":"2012","unstructured":"Lan, G., Nemirovski, A.S., Shapiro, A.: Validation analysis of mirror descent stochastic approximation method. Math. Program. 134, 425\u2013458 (2012)","journal-title":"Math. Program."},{"key":"737_CR21","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/BFb0120700","volume":"3","author":"C Lemar\u00e9chal","year":"1975","unstructured":"Lemar\u00e9chal, C.: An extension of davidon methods to non-differentiable problems. Math. Program. Study 3, 95\u2013109 (1975)","journal-title":"Math. Program. Study"},{"key":"737_CR22","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/BF01585555","volume":"69","author":"C Lemar\u00e9chal","year":"1995","unstructured":"Lemar\u00e9chal, C., Nemirovski, A.S., Nesterov, Y.E.: New variants of bundle methods. Math. Program. 69, 111\u2013148 (1995)","journal-title":"Math. Program."},{"key":"737_CR23","unstructured":"Lewis, A.S., Wright, S.J.: A Proximal Method for Composite Minimization. Manuscript, Cornell University, Ithaca, NY (2009)"},{"key":"737_CR24","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1023\/A:1021858008222","volume":"24","author":"J Linderoth","year":"2003","unstructured":"Linderoth, J., Wright, S.: Decomposition algorithms for stochastic programming on a computational grid. Comput. Optim. Appl. 24, 207\u2013250 (2003)","journal-title":"Comput. Optim. Appl."},{"key":"737_CR25","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s10479-006-6169-8","volume":"142","author":"J Linderoth","year":"2006","unstructured":"Linderoth, J., Shapiro, A., Wright, S.: The empirical behavior of sampling methods for stochastic programming. Ann. Oper. Res. 142, 215\u2013241 (2006)","journal-title":"Ann. Oper. Res."},{"key":"737_CR26","doi-asserted-by":"crossref","first-page":"1807","DOI":"10.1137\/070695915","volume":"19","author":"Z Lu","year":"2009","unstructured":"Lu, Z.: Smooth optimization approach for sparse covariance selection. SIAM J. Optim. 19, 1807\u20131827 (2009)","journal-title":"SIAM J. Optim."},{"key":"737_CR27","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0167-6377(98)00054-6","volume":"24","author":"WK Mak","year":"1999","unstructured":"Mak, W.K., Morton, D.P., Wood, R.K.: Monte carlo bounding techniques for determining solution quality in stochastic programs. Oper. Res. Lett. 24, 47\u201356 (1999)","journal-title":"Oper. Res. Lett."},{"key":"737_CR28","unstructured":"Mosek. The Mosek Optimization Toolbox for Matlab Manual. Version 6.0 (revision 93). http:\/\/www.mosek.com"},{"key":"737_CR29","unstructured":"Nemirovski, A.S., Yudin, D.: Problem Complexity and Method Efficiency in Optimization. Wiley-Interscience Series in Discrete Mathematics. Wiley, XV (1983)"},{"key":"737_CR30","unstructured":"Nemirovski, A.S.: Efficient Methods in Convex Programming. Lecture notes, Technion (1994)"},{"key":"737_CR31","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1137\/S1052623403425629","volume":"15","author":"AS Nemirovski","year":"2005","unstructured":"Nemirovski, A.S.: Prox-method with rate of convergence $$o(1\/t)$$ o ( 1 \/ t ) for variational inequalities with lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J. Optim. 15, 229\u2013251 (2005)","journal-title":"SIAM J. Optim."},{"key":"737_CR32","doi-asserted-by":"crossref","first-page":"1574","DOI":"10.1137\/070704277","volume":"19","author":"AS Nemirovski","year":"2009","unstructured":"Nemirovski, A.S., Juditsky, A., Lan, G., Shapiro, A.: Robust stochastic approximation approach to stochastic programming. SIAM J. Optim. 19, 1574\u20131609 (2009)","journal-title":"SIAM J. Optim."},{"key":"737_CR33","first-page":"356","volume":"25","author":"AS Nemirovskii","year":"1985","unstructured":"Nemirovskii, A.S., Nesterov, Y.E.: Optimal methods for smooth convex minimization. Zh. Vichisl. Mat. Fiz. 25, 356\u2013369 (1985). (In Russian)","journal-title":"Zh. Vichisl. Mat. Fiz."},{"key":"737_CR34","unstructured":"Nesterov, Y.E.: Efficient Methods in Nonlinear Programming. Radio i Sviaz, Moscow (1989)"},{"key":"737_CR35","unstructured":"Nesterov, Y.E.: Gradient methods for minimizing composite objective functions. Technical report, Center for Operations Research and Econometrics (CORE), Catholic University of Louvain, September (2007)"},{"key":"737_CR36","first-page":"543","volume":"269","author":"YE Nesterov","year":"1983","unstructured":"Nesterov, Y.E.: A method for unconstrained convex minimization problem with the rate of convergence $$O(1\/k^2)$$ O ( 1 \/ k 2 ) . Doklady AN SSSR 269, 543\u2013547 (1983)","journal-title":"Doklady AN SSSR"},{"key":"737_CR37","first-page":"509","volume":"24","author":"YE Nesterov","year":"1988","unstructured":"Nesterov, Y.E.: On an approach to the construction of optimal methods of minimization of smooth convex functions. Ekonomo. i. Mat. Metody 24, 509\u2013517 (1988)","journal-title":"Ekonomo. i. Mat. Metody"},{"key":"737_CR38","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8853-9","volume-title":"Introductory Lectures on Convex Optimization: A Basic Course","author":"YE Nesterov","year":"2004","unstructured":"Nesterov, Y.E.: Introductory Lectures on Convex Optimization: A Basic Course. Kluwer, Massachusetts (2004)"},{"key":"737_CR39","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1137\/S1052623403422285","volume":"16","author":"YE Nesterov","year":"2005","unstructured":"Nesterov, Y.E.: Excessive gap technique in nonsmooth convex minimization. SIAM J. Optim. 16, 235\u2013249 (2005)","journal-title":"SIAM J. Optim."},{"key":"737_CR40","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10107-004-0552-5","volume":"103","author":"YE Nesterov","year":"2005","unstructured":"Nesterov, Y.E.: Smooth minimization of nonsmooth functions. Math. Program. 103, 127\u2013152 (2005)","journal-title":"Math. Program."},{"key":"737_CR41","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s10107-006-0001-8","volume":"110","author":"YE Nesterov","year":"2007","unstructured":"Nesterov, Y.E.: Smoothing technique and its applications in semidefinite optimization. Math. Program. 110, 245\u2013259 (2007)","journal-title":"Math. Program."},{"issue":"2","key":"737_CR42","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1137\/100808289","volume":"21","author":"W Oliveira","year":"2011","unstructured":"Oliveira, W., Sagastiz\u00e1bal, C., Scheimberg, S.: Inexact bundle methods for two-stage stochastic programming. SIAM J. Optim. 21(2), 517\u2013544 (2011)","journal-title":"SIAM J. Optim."},{"key":"737_CR43","first-page":"12","volume":"78","author":"J Pe\u00f1a","year":"2008","unstructured":"Pe\u00f1a, J.: Nash equilibria computation via smoothing techniques. Optima 78, 12\u201313 (2008)","journal-title":"Optima"},{"key":"737_CR44","doi-asserted-by":"crossref","unstructured":"Richt\u00e1rik, P.: Approximate level method for nonsmooth convex minimization. J. Optim. Theory Appl. 152(2), 334\u2013350 (2012)","DOI":"10.1007\/s10957-011-9908-1"},{"key":"737_CR45","doi-asserted-by":"crossref","DOI":"10.1515\/9781400841059","volume-title":"Nonlinear Optimization","author":"A Ruszczy\u0144ski","year":"2006","unstructured":"Ruszczy\u0144ski, A.: Nonlinear Optimization, 1st edn. Princeton University Press, Princeton (2006)","edition":"1"},{"key":"737_CR46","unstructured":"Sagastiz\u00e1bal, C.: Nonsmooth Optimization: Thinking Outside of the Black Box. SIAG\/OPT Views-and-News, pp. 1\u20139 (2011)"},{"key":"737_CR47","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF02110042","volume":"3","author":"S Sen","year":"1994","unstructured":"Sen, S., Doverspike, R.D., Cosares, S.: Network planning with random demand. Telecommun. Syst. 3, 11\u201330 (1994)","journal-title":"Telecommun. Syst."},{"key":"737_CR48","unstructured":"Tseng, P.: On Accelerated Proximal Gradient Methods for Convex-Concave Optimization. Manuscript, University of Washington, Seattle (May 2008)"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-013-0737-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-013-0737-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-013-0737-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,13]],"date-time":"2020-08-13T00:03:06Z","timestamp":1597276986000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-013-0737-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,29]]},"references-count":48,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2015,2]]}},"alternative-id":["737"],"URL":"https:\/\/doi.org\/10.1007\/s10107-013-0737-x","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12,29]]}}}