{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T16:54:18Z","timestamp":1771520058901,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T00:00:00Z","timestamp":1676246400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T00:00:00Z","timestamp":1676246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100006192","name":"Advanced Scientific Computing Research","doi-asserted-by":"publisher","award":["DE-AC02-06CH11357"],"award-info":[{"award-number":["DE-AC02-06CH11357"]}],"id":[{"id":"10.13039\/100006192","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2024,7]]},"DOI":"10.1007\/s10957-022-02129-5","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T10:04:16Z","timestamp":1676282656000},"page":"184-203","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Accelerating Condensed Interior-Point Methods on SIMD\/GPU Architectures"],"prefix":"10.1007","volume":"202","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9009-6573","authenticated-orcid":false,"given":"Fran\u00e7ois","family":"Pacaud","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sungho","family":"Shin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michel","family":"Schanen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel Adrian","family":"Maldonado","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mihai","family":"Anitescu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,2,13]]},"reference":[{"key":"2129_CR1","unstructured":"Abadie, J., Carpentier, J.: Generalization of the wolfe reduced gradient method to the case of nonlinear constraints. In: Fletcher, R. (ed.) Optimization, pp. 37\u201347. Academic Press (1969)"},{"key":"2129_CR2","unstructured":"Babaeinejadsarookolaee, S., Birchfield, A., Christie, R.D., Coffrin, C., DeMarco, C., Diao, R., Ferris, M., Fliscounakis, S., Greene, S., Huang, R., Josz, C., Korab, R., Lesieutre, B., Maeght, J., Mak, T.W.K., Molzahn, D.K. Overbye, T.J., Panciatici, P., Park, B., Snodgrass, J., Tbaileh, A., Van Hentenryck, P., Zimmerman, R.: The power grid library for benchmarking AC optimal power flow algorithms, arXiv preprint arXiv:1908.02788, (2019)"},{"key":"2129_CR3","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1137\/0805017","volume":"5","author":"LT Biegler","year":"1995","unstructured":"Biegler, L.T., Nocedal, J., Schmid, C.: A reduced Hessian method for large-scale constrained optimization. SIAM J. Optim. 5, 314\u2013347 (1995)","journal-title":"SIAM J. Optim."},{"key":"2129_CR4","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1137\/S106482750241565X","volume":"27","author":"G Biros","year":"2005","unstructured":"Biros, G., Ghattas, O.: Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization: Part I - The Krylov-Schur Solver. SIAM J. Sci. Comput. 27, 687\u2013713 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"2129_CR5","doi-asserted-by":"publisher","first-page":"3267","DOI":"10.1109\/TPAS.1984.318568","volume":"11","author":"R Burchett","year":"1984","unstructured":"Burchett, R., Happ, H., Vierath, D.: Quadratically convergent optimal power flow. IEEE Trans. Power Appar. Syst. 11, 3267\u20133275 (1984)","journal-title":"IEEE Trans. Power Appar. Syst."},{"key":"2129_CR6","first-page":"1","volume":"1","author":"MB Cain","year":"2012","unstructured":"Cain, M.B., Oneill, R.P., Castillo, A.: History of optimal power flow and formulations. Federal Energy Regul. Comm. 1, 1\u201336 (2012)","journal-title":"Federal Energy Regul. Comm."},{"key":"2129_CR7","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.compchemeng.2015.10.010","volume":"85","author":"Y Cao","year":"2016","unstructured":"Cao, Y., Seth, A., Laird, C.D.: An augmented Lagrangian interior-point approach for large-scale NLP problems on graphics processing units. Comput. Chem. Eng. 85, 76\u201383 (2016)","journal-title":"Comput. Chem. Eng."},{"key":"2129_CR8","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/S0098-1354(00)00302-1","volume":"24","author":"AM Cervantes","year":"2000","unstructured":"Cervantes, A.M., W\u00e4chter, A., T\u00fct\u00fcnc\u00fc, R.H., Biegler, L.T.: A reduced space interior point strategy for optimization of differential algebraic systems. Comput. Chem. Eng. 24, 39\u201351 (2000)","journal-title":"Comput. Chem. Eng."},{"key":"2129_CR9","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/BF01585100","volume":"24","author":"TF Coleman","year":"1982","unstructured":"Coleman, T.F., Conn, A.R.: Nonlinear programming via an exact penalty function: Asymptotic analysis. Math. Program. 24, 123\u2013136 (1982)","journal-title":"Math. Program."},{"key":"2129_CR10","doi-asserted-by":"publisher","first-page":"1866","DOI":"10.1109\/TPAS.1968.292150","volume":"PAS\u201387","author":"H Dommel","year":"1968","unstructured":"Dommel, H., Tinney, W.: Optimal power flow solutions. IEEE Trans. Power Appar. Syst. PAS\u201387, 1866\u20131876 (1968)","journal-title":"IEEE Trans. Power Appar. Syst."},{"key":"2129_CR11","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198508380.001.0001","volume-title":"Direct Methods for Sparse Matrices","author":"IS Duff","year":"2017","unstructured":"Duff, I.S., Erisman, A.M., Reid, J.K.: Direct Methods for Sparse Matrices. Oxford University Press, Oxford (2017)"},{"key":"2129_CR12","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1137\/15M1020575","volume":"59","author":"I Dunning","year":"2017","unstructured":"Dunning, I., Huchette, J., Lubin, M.: JuMP: a modeling language for mathematical optimization. SIAM Rev. 59, 295\u2013320 (2017)","journal-title":"SIAM Rev."},{"key":"2129_CR13","volume-title":"Practical Methods of Optimization","author":"R Fletcher","year":"2013","unstructured":"Fletcher, R.: Practical Methods of Optimization. John Wiley and Sons, New Jersey (2013)"},{"key":"2129_CR14","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1287\/mnsc.36.5.519","volume":"36","author":"R Fourer","year":"1990","unstructured":"Fourer, R., Gay, D.M., Kernighan, B.W.: A modeling language for mathematical programming. Manage. Sci. 36, 519\u2013554 (1990)","journal-title":"Manage. Sci."},{"key":"2129_CR15","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s12667-012-0056-y","volume":"3","author":"S Frank","year":"2012","unstructured":"Frank, S., Steponavice, I., Rebennack, S.: Optimal power flow: a bibliographic survey I. Energy syst. 3, 221\u2013258 (2012)","journal-title":"Energy syst."},{"key":"2129_CR16","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/BF00934767","volume":"37","author":"D Gabay","year":"1982","unstructured":"Gabay, D.: Minimizing a differentiable function over a differential manifold. J. Optim. Theory Appl. 37, 177\u2013219 (1982)","journal-title":"J. Optim. Theory Appl."},{"key":"2129_CR17","doi-asserted-by":"crossref","unstructured":"Griewank, A., Walther, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM (2008)","DOI":"10.1137\/1.9780898717761"},{"key":"2129_CR18","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1137\/0910039","volume":"10","author":"CB Gurwitz","year":"1989","unstructured":"Gurwitz, C.B., Overton, M.L.: Sequential quadratic programming methods based on approximating a projected Hessian matrix. SIAM J. Sci. Stat. Comput. 10, 631\u2013653 (1989)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"2129_CR19","unstructured":"Hijazi, H., Wang, G., Coffrin, C.: Gravity: a mathematical modeling language for optimization and machine learning, Machine Learning Open Source Software Workshop at NeurIPS 2018, (2018). Available at www.gravityopt.com"},{"key":"2129_CR20","doi-asserted-by":"publisher","first-page":"1232","DOI":"10.1109\/TPWRS.2009.2037717","volume":"25","author":"Q Jiang","year":"2010","unstructured":"Jiang, Q., Geng, G.: A reduced-space interior point method for transient stability constrained optimal power flow. IEEE Trans. Power Syst. 25, 1232\u20131240 (2010)","journal-title":"IEEE Trans. Power Syst."},{"key":"2129_CR21","unstructured":"Kardos, J., Kourounis, D., Schenk, O.: Reduced-space interior point methods in power grid problems, arXiv preprint arXiv:2001.10815, (2020)"},{"key":"2129_CR22","unstructured":"Kardos, J., Kourounis, D., Schenk, O., Zimmerman, R.: Complete results for a numerical evaluation of interior point solvers for large-scale optimal power flow problems, arXiv preprint arXiv:1807.03964, (2018)"},{"key":"2129_CR23","unstructured":"Kim, Y., Pacaud, F., Kim, K., Anitescu, M.: Leveraging GPU batching for scalable nonlinear programming through massive Lagrangian decomposition, arXiv preprint arXiv:2106.14995, (2021)"},{"key":"2129_CR24","doi-asserted-by":"publisher","first-page":"3648","DOI":"10.1109\/TPWRS.2020.2975554","volume":"35","author":"D Lee","year":"2020","unstructured":"Lee, D., Turitsyn, K., Molzahn, D.K., Roald, L.A.: Feasible path identification in optimal power flow with sequential convex restriction. IEEE Trans. Power Syst. 35, 3648\u20133659 (2020)","journal-title":"IEEE Trans. Power Syst."},{"key":"2129_CR25","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1137\/0722050","volume":"22","author":"J Nocedal","year":"1985","unstructured":"Nocedal, J., Overton, M.L.: Projected Hessian updating algorithms for nonlinearly constrained optimization. SIAM J. Numer. Anal. 22, 821\u2013850 (1985)","journal-title":"SIAM J. Numer. Anal."},{"key":"2129_CR26","series-title":"Springer series in operations research","volume-title":"Numerical Optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization. Springer series in operations research, 2nd edn. Springer, New York (2006)","edition":"2"},{"key":"2129_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.epsr.2022.108268","volume":"212","author":"F Pacaud","year":"2022","unstructured":"Pacaud, F., Maldonado, D.A., Shin, S., Schanen, M., Anitescu, M.: A feasible reduced space method for real-time optimal power flow. Electric Power Syst. Res. 212, 108268 (2022)","journal-title":"Electric Power Syst. Res."},{"key":"2129_CR28","doi-asserted-by":"crossref","unstructured":"Pacaud, F., Schanen, M., Maldonado, D.A., Montoison, A., Churavy, V., Samaroo, J., Anitescu, M.: Batched second-order adjoint sensitivity for reduced space methods, In Proceedings of the 2022 SIAM Conference on Parallel Processing for Scientific Computing, SIAM, pp.\u00a060\u201371 (2022)","DOI":"10.1137\/1.9781611977141.6"},{"key":"2129_CR29","unstructured":"Revels, J., Lubin, M., Papamarkou, T.: Forward-mode automatic differentiation in Julia, arXiv preprint arXiv:1607.07892, (2016)"},{"key":"2129_CR30","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1137\/0109044","volume":"9","author":"JB Rosen","year":"1961","unstructured":"Rosen, J.B.: The gradient projection method for nonlinear programming: part II - nonlinear constraints. J. Soc. Ind. Appl. Math. 9, 514\u2013532 (1961)","journal-title":"J. Soc. Ind. Appl. Math."},{"key":"2129_CR31","unstructured":"Sargent, R.W.H.: Reduced-gradient and projection methods for nonlinear programming. In: Gill, P.E., Murray, W. (eds.) Numerical Methods for Constrained Optimization, pp. 149\u2013175. Academic Press, London (1974)"},{"key":"2129_CR32","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1016\/j.future.2003.07.011","volume":"20","author":"O Schenk","year":"2004","unstructured":"Schenk, O., G\u00e4rtner, K.: Solving unsymmetric sparse systems of linear equations with PARDISO. Futur. Gener. Comput. Syst. 20, 475\u2013487 (2004)","journal-title":"Futur. Gener. Comput. Syst."},{"key":"2129_CR33","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.jpdc.2020.05.021","volume":"144","author":"M Schubiger","year":"2020","unstructured":"Schubiger, M., Banjac, G., Lygeros, J.: GPU acceleration of ADMM for large-scale quadratic programming. J. Parallel Distrib. Comput. 144, 55\u201367 (2020)","journal-title":"J. Parallel Distrib. Comput."},{"key":"2129_CR34","doi-asserted-by":"publisher","first-page":"1156","DOI":"10.1137\/21M1391079","volume":"32","author":"S Shin","year":"2022","unstructured":"Shin, S., Anitescu, M., Zavala, V.M.: Exponential decay of sensitivity in graph-structured nonlinear programs. SIAM J. Optim. 32, 1156\u20131183 (2022)","journal-title":"SIAM J. Optim."},{"key":"2129_CR35","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1016\/j.ifacol.2021.08.322","volume":"54","author":"S Shin","year":"2021","unstructured":"Shin, S., Coffrin, C., Sundar, K., Zavala, V.M.: Graph-based modeling and decomposition of energy infrastructures. IFAC-PapersOnLine 54, 693\u2013698 (2021)","journal-title":"IFAC-PapersOnLine"},{"key":"2129_CR36","doi-asserted-by":"crossref","unstructured":"\u015awirydowicz, K., Darve, E., Jones, W., Maack, J., Regev, S., Saunders, M.A., Thomas, S.J., Pele\u0161, S.: Linear solvers for power grid optimization problems: a review of GPU-accelerated linear solvers, Parallel Comput., p.\u00a0102870 (2021)","DOI":"10.1016\/j.parco.2021.102870"},{"key":"2129_CR37","unstructured":"Tasseff, B., Coffrin, C., W\u00e4chter, A., Laird, C.: Exploring benefits of linear solver parallelism on modern nonlinear optimization applications, arXiv preprint arXiv:1909.08104, (2019)"},{"key":"2129_CR38","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A W\u00e4chter","year":"2006","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106, 25\u201357 (2006)","journal-title":"Math. Program."},{"key":"2129_CR39","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/s10107-004-0560-5","volume":"107","author":"RA Waltz","year":"2006","unstructured":"Waltz, R.A., Morales, J.L., Nocedal, J., Orban, D.: An interior algorithm for nonlinear optimization that combines line search and trust region steps. Math. Program. 107, 391\u2013408 (2006)","journal-title":"Math. Program."},{"key":"2129_CR40","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1109\/TPWRS.2010.2051168","volume":"26","author":"RD Zimmerman","year":"2010","unstructured":"Zimmerman, R.D., Murillo-S\u00e1nchez, C.E., Thomas, R.J.: MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans. Power Syst. 26, 12\u201319 (2010)","journal-title":"IEEE Trans. Power Syst."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02129-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-022-02129-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02129-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,21]],"date-time":"2024-07-21T08:03:25Z","timestamp":1721549005000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-022-02129-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,13]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,7]]}},"alternative-id":["2129"],"URL":"https:\/\/doi.org\/10.1007\/s10957-022-02129-5","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,13]]},"assertion":[{"value":"14 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 February 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}