{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T21:42:02Z","timestamp":1771623722838,"version":"3.50.1"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,2,25]],"date-time":"2023-02-25T00:00:00Z","timestamp":1677283200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,2,25]],"date-time":"2023-02-25T00:00:00Z","timestamp":1677283200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001459","name":"Ministry of Education of Singapore","doi-asserted-by":"crossref","award":["R-146-000-336-114"],"award-info":[{"award-number":["R-146-000-336-114"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2023,5]]},"DOI":"10.1007\/s10589-023-00459-2","type":"journal-article","created":{"date-parts":[[2023,2,25]],"date-time":"2023-02-25T05:03:06Z","timestamp":1677301386000},"page":"107-146","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems"],"prefix":"10.1007","volume":"85","author":[{"given":"Hong T. M.","family":"Chu","sequence":"first","affiliation":[]},{"given":"Ling","family":"Liang","sequence":"additional","affiliation":[]},{"given":"Kim-Chuan","family":"Toh","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9979-8371","authenticated-orcid":false,"given":"Lei","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,2,25]]},"reference":[{"issue":"1","key":"459_CR1","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s00245-015-9323-3","volume":"75","author":"I Abraham","year":"2017","unstructured":"Abraham, I., Abraham, R., Bergounioux, M., Carlier, G.: Tomographic reconstruction from a few views: a multi-marginal optimal transport approach. Appl. Math. Optim. 75(1), 55\u201373 (2017)","journal-title":"Appl. Math. Optim."},{"issue":"2","key":"459_CR2","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/s00032-018-0285-1","volume":"86","author":"M Bergounioux","year":"2018","unstructured":"Bergounioux, M., Abraham, I., Abraham, R., Carlier, G., Le Pennec, E., Tr\u00e9lat, E.: Variational methods for tomographic reconstruction with few views. Milan J. Math. 86(2), 157\u2013200 (2018)","journal-title":"Milan J. Math."},{"key":"459_CR3","doi-asserted-by":"crossref","unstructured":"Weber, S., Schn\u00f6rr, C., Sch\u00fcle, T., Hornegger, J.: Binary tomography by iterating linear programs. In: Geometric Properties For Incomplete Data, pp. 183\u2013197 (2006)","DOI":"10.1007\/1-4020-3858-8_10"},{"key":"459_CR4","doi-asserted-by":"crossref","unstructured":"Hol\u00fd, V., \u0160afr, K.: Disaggregating input-output tables by the multidimensional RAS method: a case study of the Czech Republic. In: To appear in Economic Systems Research (2022)","DOI":"10.1080\/09535314.2022.2091978"},{"key":"459_CR5","first-page":"3999","volume":"63","author":"A Grandy","year":"2017","unstructured":"Grandy, A., Veraart, L.: Bayesian methodology for systemic risk assessment in financial networks. Manage. Sci. 63, 3999\u20134446 (2017)","journal-title":"Manage. Sci."},{"issue":"25","key":"459_CR6","doi-asserted-by":"publisher","first-page":"10064","DOI":"10.1073\/pnas.1221333110","volume":"110","author":"J Korman","year":"2013","unstructured":"Korman, J., McCann, R.J.: Insights into capacity-constrained optimal transport. Proc. Natl. Acad. Sci. 110(25), 10064\u201310067 (2013)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"3","key":"459_CR7","doi-asserted-by":"publisher","first-page":"1501","DOI":"10.1090\/S0002-9947-2014-06032-7","volume":"367","author":"J Korman","year":"2015","unstructured":"Korman, J., McCann, R.J.: Optimal transportation with capacity constraints. Trans. Am. Math. Soc. 367(3), 1501\u20131521 (2015)","journal-title":"Trans. Am. Math. Soc."},{"issue":"5","key":"459_CR8","first-page":"1059","volume":"276","author":"VL Levin","year":"1984","unstructured":"Levin, V.L.: The problem of mass transfer in a topological space and probability measures with given marginal measures on the product of two spaces. Dokl. Akad. Nauk SSSR 276(5), 1059\u20131064 (1984)","journal-title":"Dokl. Akad. Nauk SSSR"},{"issue":"9","key":"459_CR9","doi-asserted-by":"publisher","first-page":"994","DOI":"10.1287\/mnsc.23.9.994","volume":"23","author":"J Kennington","year":"1977","unstructured":"Kennington, J., Shalaby, M.: An effective subgradient procedure for minimal cost multicommodity flow problems. Manage. Sci. 23(9), 994\u20131004 (1977)","journal-title":"Manage. Sci."},{"issue":"2","key":"459_CR10","doi-asserted-by":"publisher","first-page":"1111","DOI":"10.1137\/141000439","volume":"37","author":"J-D Benamou","year":"2015","unstructured":"Benamou, J.-D., Carlier, G., Cuturi, M., Nenna, L., Peyr\u00e9, G.: Iterative Bregman projections for regularized transportation problems. SIAM J. Sci. Comput. 37(2), 1111\u20131138 (2015)","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"459_CR11","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1080\/02331930008844513","volume":"48","author":"HH Bauschke","year":"2000","unstructured":"Bauschke, H.H., Lewis, A.S.: Dykstra\u2019s algorithm with Bregman projections: a convergence proof. Optimization 48(4), 409\u2013427 (2000)","journal-title":"Optimization"},{"issue":"384","key":"459_CR12","doi-asserted-by":"publisher","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."},{"issue":"4","key":"459_CR13","doi-asserted-by":"publisher","first-page":"402","DOI":"10.2307\/2314570","volume":"74","author":"R Sinkhorn","year":"1967","unstructured":"Sinkhorn, R.: Diagonal equivalence to matrices with prescribed row and column sums. Am. Math. Mon. 74(4), 402\u2013405 (1967)","journal-title":"Am. Math. Mon."},{"key":"459_CR14","unstructured":"Cuturi, M.: Sinkhorn distances: lightspeed computation of optimal transport. In: Advances in Neural Information Processing Systems, pp. 2292\u20132300 (2013)"},{"issue":"5\u20136","key":"459_CR15","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1561\/2200000073","volume":"11","author":"G Peyr\u00e9","year":"2019","unstructured":"Peyr\u00e9, G., Cuturi, M.: Computational optimal transport. Found. Trends Mach. Learn. 11(5\u20136), 355\u2013607 (2019)","journal-title":"Found. Trends Mach. Learn."},{"issue":"3","key":"459_CR16","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/BF00940051","volume":"73","author":"Y Censor","year":"1992","unstructured":"Censor, Y., Zenios, S.A.: Proximal minimization algorithm with $$D$$-functions. J. Optim. Theory Appl. 73(3), 451\u2013464 (1992)","journal-title":"J. Optim. Theory Appl."},{"issue":"3","key":"459_CR17","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1137\/0803026","volume":"3","author":"G Chen","year":"1993","unstructured":"Chen, G., Teboulle, M.: Convergence analysis of a proximal-like minimization algorithm using Bregman functions. SIAM J. Optim. 3(3), 538\u2013543 (1993)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"459_CR18","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1287\/moor.18.1.202","volume":"18","author":"J Eckstein","year":"1993","unstructured":"Eckstein, J.: Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming. Math. Oper. Res. 18(1), 202\u2013226 (1993)","journal-title":"Math. Oper. Res."},{"issue":"1\u20133","key":"459_CR19","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/BF02680553","volume":"83","author":"J Eckstein","year":"1998","unstructured":"Eckstein, J.: Approximate iterations in Bregman-function-based proximal algorithms. Math. Program. 83(1\u20133), 113\u2013123 (1998)","journal-title":"Math. Program."},{"issue":"1","key":"459_CR20","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/BF01592246","volume":"71","author":"A Auslender","year":"1995","unstructured":"Auslender, A., Haddou, M.: An interior-proximal method for convex linearly constrained problems and its extension to variational inequalities. Math. Program. 71(1), 77\u2013100 (1995)","journal-title":"Math. Program."},{"key":"459_CR21","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/0024-3795(90)90204-P","volume":"130","author":"PPB Eggermont","year":"1990","unstructured":"Eggermont, P.P.B.: Multiplicative iterative algorithms for convex programming. Linear Algebra Appl. 130, 25\u201342 (1990)","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"459_CR22","doi-asserted-by":"publisher","first-page":"790","DOI":"10.1287\/moor.19.4.790","volume":"19","author":"AN Iusem","year":"1994","unstructured":"Iusem, A.N., Svaiter, B.F., Teboulle, M.: Entropy-like proximal methods in convex programming. Math. Oper. Res. 19(4), 790\u2013814 (1994)","journal-title":"Math. Oper. Res."},{"issue":"3","key":"459_CR23","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1287\/moor.20.3.657","volume":"20","author":"AN Iusem","year":"1995","unstructured":"Iusem, A.N., Teboulle, M.: Convergence rate analysis of nonquadratic proximal methods for convex and linear programming. Math. Oper. Res. 20(3), 657\u2013677 (1995)","journal-title":"Math. Oper. Res."},{"issue":"3","key":"459_CR24","doi-asserted-by":"publisher","first-page":"670","DOI":"10.1287\/moor.17.3.670","volume":"17","author":"M Teboulle","year":"1992","unstructured":"Teboulle, M.: Entropic proximal mappings with applications to nonlinear programming. Math. Oper. Res. 17(3), 670\u2013690 (1992)","journal-title":"Math. Oper. Res."},{"issue":"4","key":"459_CR25","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1137\/S1052623495292130","volume":"7","author":"M Teboulle","year":"1997","unstructured":"Teboulle, M.: Convergence of proximal-like algorithms. SIAM J. Optim. 7(4), 1069\u20131083 (1997)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"459_CR26","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1007\/BF00939948","volume":"72","author":"Z-Q Luo","year":"1992","unstructured":"Luo, Z.-Q., Tseng, P.: On the convergence of the coordinate descent method for convex differentiable minimization. J. Optim. Theory Appl. 72(1), 7\u201335 (1992)","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"459_CR27","doi-asserted-by":"publisher","first-page":"846","DOI":"10.1287\/moor.18.4.846","volume":"18","author":"Z-Q Luo","year":"1993","unstructured":"Luo, Z.-Q., Tseng, P.: On the convergence rate of dual ascent methods for linearly constrained convex minimization. Math. Oper. Res. 18(4), 846\u2013867 (1993)","journal-title":"Math. Oper. Res."},{"issue":"1\u20133","key":"459_CR28","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/BF01581245","volume":"59","author":"P Tseng","year":"1993","unstructured":"Tseng, P.: Dual coordinate ascent methods for non-strictly convex minimization. Math. Program. 59(1\u20133), 231\u2013247 (1993)","journal-title":"Math. Program."},{"key":"459_CR29","unstructured":"Xie, Y., Wang, X., Wang, R., Zha, H.: A fast proximal point method for computing exact Wasserstein distance. In: Proceedings of the 35th Uncertainty in Artificial Intelligence Conference, pp. 433\u2013453 (2020)"},{"key":"459_CR30","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex analysis. Princeton University Press, Princeton (1970)"},{"issue":"3","key":"459_CR31","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/0041-5553(67)90040-7","volume":"7","author":"LM Bregman","year":"1967","unstructured":"Bregman, L.M.: The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. Math. Phys. 7(3), 200\u2013217 (1967)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"459_CR32","doi-asserted-by":"publisher","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, Heidelberg (1998)"},{"issue":"3","key":"459_CR33","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/BF00934676","volume":"34","author":"Y Censor","year":"1981","unstructured":"Censor, Y., Lent, A.: An iterative row-action method for interval convex programming. J. Optim. Theory Appl. 34(3), 321\u2013353 (1981)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"459_CR34","first-page":"27","volume":"4","author":"HH Bauschke","year":"1997","unstructured":"Bauschke, H.H., Borwein, J.M.: Legendre functions and the method of random Bregman projections. J. Convex Anal. 4(1), 27\u201367 (1997)","journal-title":"J. Convex Anal."},{"key":"459_CR35","volume-title":"Introduction to optimization","author":"BT Polyak","year":"1987","unstructured":"Polyak, B.T.: Introduction to optimization. Optimization Software Inc., New York (1987)"},{"key":"459_CR36","unstructured":"Tibshirani, R.J.: Dykstra\u2019s algorithm, ADMM, and coordinate descent: Connections, insights, and extensions. In: Advances in Neural Information Processing Systems, pp. 517\u2013528 (2017)"},{"issue":"4","key":"459_CR37","doi-asserted-by":"publisher","first-page":"263","DOI":"10.6028\/jres.049.027","volume":"49","author":"AJ Hoffman","year":"1952","unstructured":"Hoffman, A.J.: On approximate solutions of systems of linear inequalities. J. Res. Natl. Bur. Stand. 49(4), 263\u2013265 (1952)","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"459_CR38","first-page":"1","volume":"23","author":"T Lin","year":"2022","unstructured":"Lin, T., Ho, N., Cuturi, M., Jordan, M.I.: On the complexity of approximating multimarginal optimal transport. J. Mach. Learn. Res. 23, 1\u201343 (2022)","journal-title":"J. Mach. Learn. Res."},{"key":"459_CR39","unstructured":"Altschuler, J., Weed, J., Rigollet, P.: Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration. In: Advances in Neural Information Processing Systems, 30 (2017)"},{"key":"459_CR40","volume-title":"Introduction to linear optimization","author":"D Bertsimas","year":"1997","unstructured":"Bertsimas, D., Tsitsiklis, J.N.: Introduction to linear optimization. Athena Scientific, MIT (1997)"},{"issue":"4","key":"459_CR41","first-page":"349","volume":"7","author":"SS Nielsen","year":"1993","unstructured":"Nielsen, S.S., Zenios, S.A.: Massively parallel proximal algorithms for solving linear stochastic network programs. The Int. J. Supercomput. Appl. 7(4), 349\u2013364 (1993)","journal-title":"The Int. J. Supercomput. Appl."},{"issue":"3","key":"459_CR42","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/BF02592213","volume":"73","author":"SS Nielsen","year":"1996","unstructured":"Nielsen, S.S., Zenios, S.A.: Solving multistage stochastic network programs on massively parallel computers. Math. Program. 73(3), 227\u2013250 (1996)","journal-title":"Math. Program."},{"key":"459_CR43","doi-asserted-by":"publisher","DOI":"10.1515\/9781400841059","volume-title":"Nonlinear optimization","author":"A Ruszczy\u0144ski","year":"2006","unstructured":"Ruszczy\u0144ski, A.: Nonlinear optimization. Princeton University Press, Princeton (2006)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-023-00459-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-023-00459-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-023-00459-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,5]],"date-time":"2023-04-05T16:48:43Z","timestamp":1680713323000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-023-00459-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,25]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,5]]}},"alternative-id":["459"],"URL":"https:\/\/doi.org\/10.1007\/s10589-023-00459-2","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,25]]},"assertion":[{"value":"29 November 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 February 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}