{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T16:22:34Z","timestamp":1775492554213,"version":"3.50.1"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2018,1,29]],"date-time":"2018-01-29T00:00:00Z","timestamp":1517184000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"CONICYT","award":["Fondecyt 1151003, Basal PFB-03 and Basal FB0003"],"award-info":[{"award-number":["Fondecyt 1151003, Basal PFB-03 and Basal FB0003"]}]},{"name":"CONICYT","award":["Fondecyt 1150909, Basal PFB-03 and Basal FB0003, CONICYT-PCHA\/doctorado Nacional\/2014-21140621"],"award-info":[{"award-number":["Fondecyt 1150909, Basal PFB-03 and Basal FB0003, CONICYT-PCHA\/doctorado Nacional\/2014-21140621"]}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"crossref","award":["Project B04 in the Sonderforschungsbereich \/ Transregio 154 Mathematical Modelling, Sim- ulation and Optimization using the Example of Gas Networks."],"award-info":[{"award-number":["Project B04 in the Sonderforschungsbereich \/ Transregio 154 Mathematical Modelling, Sim- ulation and Optimization using the Example of Gas Networks."]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2019,3]]},"DOI":"10.1007\/s10107-018-1237-9","type":"journal-article","created":{"date-parts":[[2018,1,29]],"date-time":"2018-01-29T04:19:36Z","timestamp":1517199576000},"page":"167-194","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Subdifferential characterization of probability functions under Gaussian distribution"],"prefix":"10.1007","volume":"174","author":[{"given":"Abderrahim","family":"Hantoute","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ren\u00e9","family":"Henrion","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pedro","family":"P\u00e9rez-Aros","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,1,29]]},"reference":[{"key":"1237_CR1","doi-asserted-by":"publisher","first-page":"2821","DOI":"10.1090\/S0025-5718-2014-02839-1","volume":"83","author":"JS Brauchart","year":"2014","unstructured":"Brauchart, J.S., Saff, E.B., Sloan, I.H., Womersley, R.S.: QMC designs: optimal order quasi Monte Carlo integration schemes on the sphere. Math. Comput. 83, 2821\u20132851 (2014)","journal-title":"Math. Comput."},{"key":"1237_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0087685","volume-title":"Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics","author":"C Castaing","year":"1977","unstructured":"Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol. 580. Springer, Berlin (1977)"},{"key":"1237_CR3","volume-title":"Optimization and Nonsmooth Analysis Classics in Applied Mathematics","author":"FH Clarke","year":"1987","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis Classics in Applied Mathematics, vol. 5. Society for Industrial and Applied Mathematics, New York (1987)"},{"key":"1237_CR4","unstructured":"Correa, R., Hantoute, A., P\u00e9rez-Aros, P.: Sequential and exact formulae for the subdifferential of nonconvex integrand functionals, submitted"},{"key":"1237_CR5","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1023\/A:1019215116991","volume":"100","author":"I De\u00e1k","year":"2000","unstructured":"De\u00e1k, I.: Subroutines for computing normal probabilities of sets\u2014computer experiences. Ann. Oper. Res. 100, 103\u2013122 (2000)","journal-title":"Ann. Oper. Res."},{"key":"1237_CR6","volume-title":"Structural Reliability Method","author":"O Ditlevsen","year":"1996","unstructured":"Ditlevsen, O., Madsen, H.O.: Structural Reliability Method. Wiley, New York (1996)"},{"key":"1237_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01689-9","volume-title":"Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics","author":"A Genz","year":"2009","unstructured":"Genz, A., Bretz, F.: Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, vol. 195. Springer, Dordrecht (2009)"},{"key":"1237_CR8","unstructured":"Gonz\u00e1lez Grand\u00f3n, T., Heitsch, H., Henrion, R.: A joint model of probabilistic\/robust constraints with application to stationary gas networks, submitted"},{"key":"1237_CR9","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/s00186-016-0564-y","volume":"84","author":"C Gotzes","year":"2016","unstructured":"Gotzes, C., Heitsch, H., Henrion, R., Schultz, R.: Feasibility of nominations in stationary gas networks with random load. Math. Methods Oper. Res. 84, 427\u2013457 (2016)","journal-title":"Math. Methods Oper. Res."},{"key":"1237_CR10","doi-asserted-by":"publisher","first-page":"1101","DOI":"10.1080\/07362999808809581","volume":"16","author":"AI Kibzun","year":"1998","unstructured":"Kibzun, A.I., Uryas\u2019ev, S.: Differentiability of probability function. Stoch. Anal. Appl. 16, 1101\u20131128 (1998)","journal-title":"Stoch. Anal. Appl."},{"key":"1237_CR11","doi-asserted-by":"publisher","first-page":"3325","DOI":"10.1023\/A:1023673105317","volume":"116","author":"AY Kruger","year":"2003","unstructured":"Kruger, A.Y.: On Fr\u00e9chet subdifferentials. J. Math. Sci. 116, 3325\u20133358 (2003)","journal-title":"J. Math. Sci."},{"key":"1237_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-31247-1","volume-title":"Variational Analysis and Generalized Differentiation. Vol. 1: Basic Theory, Vol. 2: Applications","author":"BS Mordukhovich","year":"2006","unstructured":"Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation. Vol. 1: Basic Theory, Vol. 2: Applications. Springer, Berlin (2006)"},{"key":"1237_CR13","doi-asserted-by":"publisher","first-page":"898","DOI":"10.1137\/S1052623403431639","volume":"15","author":"GC Pflug","year":"2005","unstructured":"Pflug, G.C., Weisshaupt, H.: Probability gradient estimation by set-valued calculus and applications in network design. SIAM J. Optim. 15, 898\u2013914 (2005)","journal-title":"SIAM J. Optim."},{"key":"1237_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3087-7","volume-title":"Stochastic Programming","author":"A Pr\u00e9kopa","year":"1995","unstructured":"Pr\u00e9kopa, A.: Stochastic Programming. Kluwer, Dordrecht (1995)"},{"key":"1237_CR15","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/0022-247X(84)90204-X","volume":"102","author":"P Pucci","year":"1984","unstructured":"Pucci, P., Vitillaro, G.: A representation theorem for Aumann integrals. J. Math. Anal. Appl. 102, 86\u2013101 (1984)","journal-title":"J. Math. Anal. Appl."},{"key":"1237_CR16","volume-title":"Variational Analysis","author":"RT Rockafellar","year":"1997","unstructured":"Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin (1997)"},{"key":"1237_CR17","doi-asserted-by":"crossref","unstructured":"Shapiro, A., Dentcheva, D., Ruszczy\u0144ski, A.: Lectures on Stochastic Programming. MPS-SIAM series on optimization, vol. 9 (2009)","DOI":"10.1137\/1.9780898718751"},{"key":"1237_CR18","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/0377-0427(94)90388-3","volume":"56","author":"S Uryas\u2019ev","year":"1994","unstructured":"Uryas\u2019ev, S.: Derivatives of probability functions and integrals over sets given by inequalities. J. Comput. Appl. Math. 56, 197\u2013223 (1994)","journal-title":"J. Comput. Appl. Math."},{"key":"1237_CR19","doi-asserted-by":"publisher","first-page":"1864","DOI":"10.1137\/130922689","volume":"24","author":"W Ackooij Van","year":"2014","unstructured":"Van Ackooij, W., Henrion, R.: Gradient formulae for nonlinear probabilistic constraints with Gaussian and Gaussian-like distributions. SIAM J. Optim. 24, 1864\u20131889 (2014)","journal-title":"SIAM J. Optim."},{"key":"1237_CR20","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1137\/16M1061308","volume":"5","author":"W Ackooij Van","year":"2017","unstructured":"Van Ackooij, W., Henrion, R.: (Sub-) Gradient formulae for probability functions of random inequality systems under Gaussian distribution. SIAM\/ASA J. Uncertain. Quantif. 5, 63\u201387 (2017)","journal-title":"SIAM\/ASA J. Uncertain. Quantif."},{"key":"1237_CR21","first-page":"573","volume-title":"Handbook for Operations Research and Management Sciences","author":"RJ-B Wets","year":"1989","unstructured":"Wets, R.J.-B.: Stochastic programming. In: Nemhauser, G., Rinnooy Kan, A., Todd, M. (eds.) Handbook for Operations Research and Management Sciences, vol. 1, pp. 573\u2013629. Elsevier, Amsterdam (1989)"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-018-1237-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-018-1237-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-018-1237-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,13]],"date-time":"2022-08-13T09:54:58Z","timestamp":1660384498000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-018-1237-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,29]]},"references-count":21,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["1237"],"URL":"https:\/\/doi.org\/10.1007\/s10107-018-1237-9","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,29]]},"assertion":[{"value":"21 February 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 January 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}