{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T00:57:04Z","timestamp":1782349024491,"version":"3.54.5"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T00:00:00Z","timestamp":1723161600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T00:00:00Z","timestamp":1723161600000},"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":["Math. Prog. Comp."],"published-print":{"date-parts":[[2024,9]]},"DOI":"10.1007\/s12532-024-00259-7","type":"journal-article","created":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T05:02:28Z","timestamp":1723179748000},"page":"337-367","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["PEPit: computer-assisted worst-case analyses of first-order optimization methods in Python"],"prefix":"10.1007","volume":"16","author":[{"given":"Baptiste","family":"Goujaud","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C\u00e9line","family":"Moucer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fran\u00e7ois","family":"Glineur","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julien M.","family":"Hendrickx","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adrien B.","family":"Taylor","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aymeric","family":"Dieuleveut","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,8,9]]},"reference":[{"issue":"6","key":"259_CR1","doi-asserted-by":"publisher","first-page":"1649","DOI":"10.1007\/s11590-021-01821-1","volume":"16","author":"H Abbaszadehpeivasti","year":"2022","unstructured":"Abbaszadehpeivasti, H., de Klerk, E., Zamani, M.: The exact worst-case convergence rate of the gradient method with fixed step lengths for $$L$$-smooth functions. Optim. Lett. 16(6), 1649\u20131661 (2022)","journal-title":"Optim. Lett."},{"key":"259_CR2","doi-asserted-by":"crossref","unstructured":"Bousselmi, N., Hendrickx, J.M., Glineur, F.: Interpolation conditions for linear operators and applications to performance estimation problems. arXiv:2302.08781 (2023)","DOI":"10.1137\/23M1575391"},{"key":"259_CR3","doi-asserted-by":"crossref","unstructured":"Colla, S., Hendrickx, J.M.: Automated worst-case performance analysis of decentralized gradient descent. In: Proceedings of the 60th Conference on Decision and Control (CDC) (2021)","DOI":"10.1109\/CDC45484.2021.9683505"},{"key":"259_CR4","unstructured":"Defazio, A.: A simple practical accelerated method for finite sums. In: Advances in Neural Information Processing Systems (NIPS) (2016)"},{"issue":"1","key":"259_CR5","first-page":"2909","volume":"17","author":"S Diamond","year":"2016","unstructured":"Diamond, S., Boyd, S.: CVXPY: a Python-embedded modeling language for convex optimization. J. Mach. Learn. Res. (JMLR) 17(1), 2909\u20132913 (2016)","journal-title":"J. Mach. Learn. Res. (JMLR)"},{"key":"259_CR6","unstructured":"Drori, Y.: Contributions to the complexity analysis of optimization algorithms. Ph.D. thesis, Tel-Aviv University (2014)"},{"issue":"1","key":"259_CR7","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/s10107-013-0653-0","volume":"145","author":"Y Drori","year":"2014","unstructured":"Drori, Y., Teboulle, M.: Performance of first-order methods for smooth convex minimization: a novel approach. Math. Program. 145(1), 451\u2013482 (2014)","journal-title":"Math. Program."},{"key":"259_CR8","doi-asserted-by":"crossref","unstructured":"d\u2019Aspremont, A., Scieur, D., Taylor, A.: Acceleration methods. Foundations and Trends\u00ae in Optimization 5(1\u20132), 1\u2013245 (2021)","DOI":"10.1561\/2400000036"},{"key":"259_CR9","doi-asserted-by":"crossref","unstructured":"Fazel, M., Hindi, H., Boyd, S.P.: Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices. In: American Control Conference (ACC), vol. 3, pp. 2156\u20132162. IEEE (2003)","DOI":"10.1109\/ACC.2003.1243393"},{"issue":"3","key":"259_CR10","doi-asserted-by":"publisher","first-page":"2654","DOI":"10.1137\/17M1136845","volume":"28","author":"M Fazlyab","year":"2018","unstructured":"Fazlyab, M., Ribeiro, A., Morari, M., Preciado, V.M.: Analysis of optimization algorithms via integral quadratic constraints: nonstrongly convex problems. SIAM J. Optim. 28(3), 2654\u20132689 (2018)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"259_CR11","doi-asserted-by":"publisher","first-page":"975","DOI":"10.1007\/s10107-021-01665-8","volume":"194","author":"O Gannot","year":"2022","unstructured":"Gannot, O.: A frequency-domain analysis of inexact gradient methods. Math. Program. 194(1), 975\u20131016 (2022)","journal-title":"Math. Program."},{"key":"259_CR12","unstructured":"Gorbunov, E., Loizou, N., Gidel, G.: Extragradient method: $$o(1\/k)$$ last-iterate convergence for monotone variational inequalities and connections with cocoercivity. In: International Conference on Artificial Intelligence and Statistics (AISTATS), pp. 366\u2013402 (2022)"},{"key":"259_CR13","doi-asserted-by":"publisher","first-page":"2485","DOI":"10.1109\/LCSYS.2023.3286277","volume":"7","author":"B Goujaud","year":"2023","unstructured":"Goujaud, B., Dieuleveut, A., Taylor, A.: Counter-examples in first-order optimization: a constructive approach. IEEE Control Syst. Lett. 7, 2485\u20132490 (2023)","journal-title":"IEEE Control Syst. Lett."},{"issue":"3","key":"259_CR14","doi-asserted-by":"publisher","first-page":"1905","DOI":"10.1137\/19M1299049","volume":"30","author":"G Gu","year":"2020","unstructured":"Gu, G., Yang, J.: Tight sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. SIAM J. Optim. 30(3), 1905\u20131921 (2020)","journal-title":"SIAM J. Optim."},{"key":"259_CR15","unstructured":"Hu, B., Wright, S., Lessard, L.: Dissipativity theory for accelerating stochastic variance reduction: a unified analysis of SVRG and Katyusha using semidefinite programs. In: International Conference on Machine Learning (ICML) (2018)"},{"issue":"1","key":"259_CR16","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s10107-021-01643-0","volume":"190","author":"D Kim","year":"2021","unstructured":"Kim, D.: Accelerated proximal point method for maximally monotone operators. Math. Program. 190(1), 57\u201387 (2021)","journal-title":"Math. Program."},{"issue":"1\u20132","key":"259_CR17","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/s10107-015-0949-3","volume":"159","author":"D Kim","year":"2016","unstructured":"Kim, D., Fessler, J.A.: Optimized first-order methods for smooth convex minimization. Math. Program. 159(1\u20132), 81\u2013107 (2016)","journal-title":"Math. Program."},{"issue":"1","key":"259_CR18","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1007\/s10957-020-01770-2","volume":"188","author":"D Kim","year":"2021","unstructured":"Kim, D., Fessler, J.A.: Optimizing the efficiency of first-order methods for decreasing the gradient of smooth convex functions. J. Optim. Theory Appl. 188(1), 192\u2013219 (2021)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"259_CR19","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1137\/15M1009597","volume":"26","author":"L Lessard","year":"2016","unstructured":"Lessard, L., Recht, B., Packard, A.: Analysis and design of optimization algorithms via integral quadratic constraints. SIAM J. Optim. 26(1), 57\u201395 (2016)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"259_CR20","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1007\/s11590-020-01617-9","volume":"15","author":"F Lieder","year":"2021","unstructured":"Lieder, F.: On the convergence rate of the Halpern-iteration. Optim. Lett. 15(2), 405\u2013418 (2021)","journal-title":"Optim. Lett."},{"key":"259_CR21","unstructured":"Mosek, A.: The MOSEK optimization software. Online at http:\/\/www.mosek.com 54 (2010)"},{"key":"259_CR22","unstructured":"Nemirovski, A.: Information-based complexity of convex programming. Lecture notes. http:\/\/www2.isye.gatech.edu\/~nemirovs\/Lec_EMCO.pdf (1994)"},{"issue":"2","key":"259_CR23","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/0885-064X(92)90013-2","volume":"8","author":"AS Nemirovsky","year":"1992","unstructured":"Nemirovsky, A.S.: Information-based complexity of linear operator equations. J. Complex. 8(2), 153\u2013175 (1992)","journal-title":"J. Complex."},{"issue":"2","key":"259_CR24","first-page":"372","volume":"27","author":"Y Nesterov","year":"1983","unstructured":"Nesterov, Y.: A method of solving a convex programming problem with convergence rate $${O}(1\/k^2)$$. Soviet Math. Doklady 27(2), 372\u2013376 (1983)","journal-title":"Soviet Math. Doklady"},{"key":"259_CR25","volume-title":"Introductory Lectures on Convex Optimization","author":"Y Nesterov","year":"2003","unstructured":"Nesterov, Y.: Introductory Lectures on Convex Optimization. Springer, Cham (2003)"},{"issue":"3","key":"259_CR26","doi-asserted-by":"publisher","first-page":"1042","DOI":"10.1007\/s10957-016-0892-3","volume":"169","author":"B O\u2019Donoghue","year":"2016","unstructured":"O\u2019Donoghue, B., Chu, E., Parikh, N., Boyd, S.: Conic optimization via operator splitting and homogeneous self-dual embedding. J. Optim. Theory Appl. 169(3), 1042\u20131068 (2016)","journal-title":"J. Optim. Theory Appl."},{"key":"259_CR27","doi-asserted-by":"crossref","unstructured":"Patrinos, P., Stella, L., Bemporad, A.: Douglas\u2013Rachford splitting: complexity estimates and accelerated variants. In: Proceedings of the 53rd Conference on Decision and Control (CDC) (2014)","DOI":"10.1109\/CDC.2014.7040049"},{"issue":"3","key":"259_CR28","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1137\/070697835","volume":"52","author":"B Recht","year":"2010","unstructured":"Recht, B., Fazel, M., Parrilo, P.A.: Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev. 52(3), 471\u2013501 (2010)","journal-title":"SIAM Rev."},{"issue":"3","key":"259_CR29","doi-asserted-by":"publisher","first-page":"2251","DOI":"10.1137\/19M1304854","volume":"30","author":"EK Ryu","year":"2020","unstructured":"Ryu, E.K., Taylor, A.B., Bergeling, C., Giselsson, P.: Operator splitting performance estimation: tight contraction factors and optimal parameter selection. SIAM J. Optim. 30(3), 2251\u20132271 (2020)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"259_CR30","doi-asserted-by":"publisher","first-page":"1597","DOI":"10.1109\/TCNS.2020.2988009","volume":"7","author":"A Sundararajan","year":"2020","unstructured":"Sundararajan, A., Van Scoy, B., Lessard, L.: Analysis and design of first-order distributed optimization algorithms over time-varying graphs. IEEE Trans. Control Netw. Syst. 7(4), 1597\u20131608 (2020)","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"259_CR31","unstructured":"Taylor, A., Bach, F.: Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functions. In: Proceedings of the 32nd Conference on Learning Theory (COLT) (2019)"},{"issue":"1\u20132","key":"259_CR32","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/s10107-022-01839-y","volume":"199","author":"A Taylor","year":"2023","unstructured":"Taylor, A., Drori, Y.: An optimal gradient method for smooth strongly convex minimization. Math. Program. 199(1\u20132), 557\u2013594 (2023)","journal-title":"Math. Program."},{"key":"259_CR33","unstructured":"Taylor, A., Van\u00a0Scoy, B., Lessard, L.: Lyapunov functions for first-order methods: tight automated convergence guarantees. In: International Conference on Machine Learning (ICML) (2018)"},{"issue":"3","key":"259_CR34","doi-asserted-by":"publisher","first-page":"1283","DOI":"10.1137\/16M108104X","volume":"27","author":"AB Taylor","year":"2017","unstructured":"Taylor, A.B., Hendrickx, J.M., Glineur, F.: Exact worst-case performance of first-order methods for composite convex optimization. SIAM J. Optim. 27(3), 1283\u20131313 (2017)","journal-title":"SIAM J. Optim."},{"key":"259_CR35","doi-asserted-by":"crossref","unstructured":"Taylor, A.B., Hendrickx, J.M., Glineur, F.: Performance estimation toolbox (PESTO): automated worst-case analysis of first-order optimization methods. In: Proceedings of the 56th Conference on Decision and Control (CDC) (2017)","DOI":"10.1109\/CDC.2017.8263832"},{"issue":"1\u20132","key":"259_CR36","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s10107-016-1009-3","volume":"161","author":"AB Taylor","year":"2017","unstructured":"Taylor, A.B., Hendrickx, J.M., Glineur, F.: Smooth strongly convex interpolation and exact worst-case performance of first-order methods. Math. Program. 161(1\u20132), 307\u2013345 (2017)","journal-title":"Math. Program."},{"key":"259_CR37","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/s10957-018-1298-1","volume":"178","author":"AB Taylor","year":"2018","unstructured":"Taylor, A.B., Hendrickx, J.M., Glineur, F.: Exact worst-case convergence rates of the proximal gradient method for composite convex minimization. J. Optim. Theory Appl. 178, 455\u2013476 (2018)","journal-title":"J. Optim. Theory Appl."},{"key":"259_CR38","doi-asserted-by":"crossref","unstructured":"Upadhyaya, M., Banert, S., Taylor, A.B., Giselsson, P.: Automated tight Lyapunov analysis for first-order methods. arXiv:2302.06713 (2023)","DOI":"10.1007\/s10107-024-02061-8"},{"issue":"1","key":"259_CR39","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1109\/LCSYS.2017.2722406","volume":"2","author":"B Van Scoy","year":"2017","unstructured":"Van Scoy, B., Freeman, R.A., Lynch, K.M.: The fastest known globally convergent first-order method for minimizing strongly convex functions. IEEE Control Syst. Lett. 2(1), 49\u201354 (2017)","journal-title":"IEEE Control Syst. Lett."}],"container-title":["Mathematical Programming Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-024-00259-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12532-024-00259-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-024-00259-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,23]],"date-time":"2024-09-23T07:27:14Z","timestamp":1727076434000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12532-024-00259-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,9]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["259"],"URL":"https:\/\/doi.org\/10.1007\/s12532-024-00259-7","relation":{},"ISSN":["1867-2949","1867-2957"],"issn-type":[{"value":"1867-2949","type":"print"},{"value":"1867-2957","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,9]]},"assertion":[{"value":"16 December 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 May 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 August 2024","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"}},{"value":"The full code is publicly available at , downloadable using the shell command line <scp>pip install pepit<\/scp>, and its documentation can be found at .","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability."}}]}}