{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T16:47:46Z","timestamp":1790009266148,"version":"4.0.1"},"reference-count":38,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"Gaspard-Monge program for Optimization and Operations Research"},{"DOI":"10.13039\/501100000921","name":"European Cooperation in Science and Technology","doi-asserted-by":"publisher","award":["TD1207"],"award-info":[{"award-number":["TD1207"]}],"id":[{"id":"10.13039\/501100000921","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We propose a family of proximal bundle methods for minimizing sum-structured convex nondifferentiable functions which require two slightly uncommon assumptions that are satisfied in many relevant applications: Lipschitz continuity of the functions and oracles which also produce upper estimates on the function values. In exchange, the methods: (i) use upper models of the functions that allow one to estimate function values at points where the oracle has not been called; (ii) provide the oracles with more information about when the function computation can be interrupted, possibly diminishing their cost; (iii) allow one to skip oracle calls entirely for some of the component functions, not only at \u201cnull steps\u201d but also at \u201cserious steps''; (iv) provide explicit and reliable a posteriori estimates of the quality of the obtained solutions; (v) work with all possible combinations of different assumptions on how the oracles deal with not being able to compute the function with arbitrary accuracy. We also discuss the introduction of constraints (or, more generally, of easy components) and use of (partly) aggregated models.<\/jats:p>","DOI":"10.1137\/16m1089897","type":"journal-article","created":{"date-parts":[[2018,2,6]],"date-time":"2018-02-06T12:33:02Z","timestamp":1517920382000},"page":"379-410","source":"Crossref","is-referenced-by-count":24,"title":["Incremental Bundle Methods using Upper Models"],"prefix":"10.1137","volume":"28","author":[{"given":"Wim","family":"van Ackooij","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antonio","family":"Frangioni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,2,6]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/120888867"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/100817930"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"A. Astorino, M. Gaudioso, and E. Gorgone,\n                      A method for convex minimization based on translated first-order approximations\n                      , Numer. Algorithms, (2017), pp. 1-16,https:\/\/doi.org\/10.1007\/s11075-017-0280-6.","DOI":"10.1007\/s11075-017-0280-6"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011202900805"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-006-0079-z"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-014-0808-7"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585170"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(00)00310-3"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/080718814"},{"key":"atypb10","unstructured":"W. de Oliveira and J. Eckstein,\n                      A Bundle Method for Exploiting Additive Structure in Difficult Optimization Problems\n                      , Optimization Online, 2015."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2013.871282"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-014-0809-6"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/100808289"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-005-0593-4"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-009-9288-8"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/0305-0548(96)00006-8"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-005-3447-9"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2007.10.003"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-013-0642-3"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-017-0120-7"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1050.0175"},{"key":"atypb22","unstructured":"C. Helmberg,\n                      Numerical experiments on dynamically choosing cutting models in bundle methods\n                      , in Proceedings of the International Workshop on Optimization Challenges in the Evolution of Energy Networks to Smart Grids, 2016."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1060.0374"},{"key":"atypb24","unstructured":"J. Hiriart-Urruty and C. Lemare\u0301chal,\n                      Convex Analysis and Minimization Algorithms\n                      I, 2nd ed., Grundlehren Math. Wiss. 305, Springer-Verlag, Berlin, 1996."},{"key":"atypb25","unstructured":"J. Hiriart-Urruty and C. Lemare\u0301chal,\n                      Convex Analysis and Minimization Algorithms\n                      II, 2nd ed., Grundlehren Math. Wiss. 306, Springer-Verlag, Berlin, 1996."},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585162"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1137\/040603929"},{"key":"atypb28","first-page":"112","author":"Lemare\u0301chal C.","year":"2001","journal-title":"Berlin"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1007\/PL00011429"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1137\/140967337"},{"key":"atypb31","doi-asserted-by":"crossref","unstructured":"M. Tahanan, W. van Ackooij, A. Frangioni, and F. Lacalandra,\n                      Large-scale unit commitment under uncertainty: A literature survey\n                      , 4OR, 13 (2015), pp. 115-171,https:\/\/doi.org\/10.1007\/s10288-014-0279-y.","DOI":"10.1007\/s10288-014-0279-y"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2016.08.002"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-013-9610-3"},{"key":"atypb34","first-page":"57","volume":"130","author":"van Ackooij W.","year":"2017","journal-title":"Informs J. Comput."},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-016-9851-z"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-015-2029-8"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1137\/120903099"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2014.05.010"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1089897","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:15:16Z","timestamp":1787336116000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1089897"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/16M1089897"],"URL":"https:\/\/doi.org\/10.1137\/16m1089897","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}