{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T11:10:04Z","timestamp":1751368204898,"version":"3.41.0"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[1998,4,1]],"date-time":"1998-04-01T00:00:00Z","timestamp":891388800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1998,4,1]],"date-time":"1998-04-01T00:00:00Z","timestamp":891388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Global Optimization"],"published-print":{"date-parts":[[1998,4]]},"DOI":"10.1023\/a:1008213919383","type":"journal-article","created":{"date-parts":[[2002,12,22]],"date-time":"2002-12-22T13:47:34Z","timestamp":1040564854000},"page":"225-237","source":"Crossref","is-referenced-by-count":4,"title":["The Global Optimization of Variational Problems with Discontinuous Solutions"],"prefix":"10.1007","volume":"12","author":[{"given":"J. E.","family":"Rubio","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"146137_CR1","doi-asserted-by":"crossref","first-page":"673","DOI":"10.4153\/CJM-1992-041-2","volume":"44","author":"J. M. Aldaz","year":"1992","unstructured":"Aldaz, J. M. (1992). A characterization of universal Loeb measurability for completely regular Hausdorff spaces. Canadian Journal of Mathematics, 44: 673\u2013690.","journal-title":"Canadian Journal of Mathematics"},{"key":"146137_CR2","unstructured":"Berge, C. (1963). Topological Spaces. Oliver and Boyd."},{"key":"146137_CR3","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1137\/0331057","volume":"31","author":"A. Bressan","year":"1993","unstructured":"Bressan, A. and Rampazzo, F. (1993). On differential systems with quadratic impulses and their application to Lagrangian mechanics. SIAM Journal on Control and Optimization, 31: 1205\u20131220.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"146137_CR4","unstructured":"Choquet, G. (1969). Lectures on Analysis. Benjamin."},{"key":"146137_CR5","doi-asserted-by":"crossref","unstructured":"Cutland, N. J., editor (1988). Nonstandard Analysis and its Applications. Cambridge University Press.","DOI":"10.1017\/CBO9781139172110"},{"key":"146137_CR6","doi-asserted-by":"crossref","first-page":"663","DOI":"10.4153\/CJM-1979-066-0","volume":"31","author":"C. W. Henson","year":"1979","unstructured":"Henson, C. W. (1979). Analytic sets, Baire sets and the standard part map. Canadian Journal of Mathematics, 31: 663\u2013672.","journal-title":"Canadian Journal of Mathematics"},{"key":"146137_CR7","first-page":"231","volume":"2","author":"V. F. Krotov","year":"1961","unstructured":"Krotov, V. F. (1961). The principal problem of the calculus of variations for the simplest functional on a set of discontinuous functions. Soviet Mathematics, 2: 231\u2013234.","journal-title":"Soviet Mathematics"},{"key":"146137_CR8","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1090\/S0002-9947-1987-0906814-1","volume":"304","author":"D. Landers","year":"1987","unstructured":"Landers, D. and Rogge, L. (1987). Universal Loeb-measurability of sets and of the standard part map with applications. Transactions of the American Mathematical Society, 304: 229\u2013243.","journal-title":"Transactions of the American Mathematical Society"},{"key":"146137_CR9","first-page":"27","volume":"1","author":"D. F. Lawden","year":"1959","unstructured":"Lawden, D. F. (1959). Discontinuous solutions of variational problems. Journal of the Autralian Mathematical Society, 1: 27\u201337.","journal-title":"Journal of the Autralian Mathematical Society"},{"key":"146137_CR10","unstructured":"Monroe, M. E. (1953). Introduction to Measure and Integration. Addison-Wesley."},{"key":"146137_CR11","unstructured":"Oberguggenberger, M. (1992). Multiplication of Distributions and Applications to Partial Differential Equations. Longman."},{"key":"146137_CR12","doi-asserted-by":"crossref","first-page":"61","DOI":"10.7146\/math.scand.a-12437","volume":"72","author":"H. Render","year":"1993","unstructured":"Render, H. (1993). Pushing down Loeb measures. Mathematica Scandinavica, 72: 61\u201384.","journal-title":"Mathematica Scandinavica"},{"key":"146137_CR13","doi-asserted-by":"crossref","first-page":"183","DOI":"10.24033\/bsmf.1429","volume":"80","author":"P. C. Rosenbloom","year":"1952","unstructured":"Rosenbloom, P. C. (1952). Quelques classes de probl\u00e8mes \u00e9xtremaux. Bulletin de la Societ\u00e9 Math\u00e9matique de France, 80: 183\u2013216.","journal-title":"Bulletin de la Societ\u00e9 Math\u00e9matique de France"},{"key":"146137_CR14","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF00934053","volume":"19","author":"J. E. Rubio","year":"1976","unstructured":"Rubio, J. E. (1976). An existence theorem in the calculus of variations. Journal of Optimization Theory and its Applications, 19: 81\u201387.","journal-title":"Journal of Optimization Theory and its Applications"},{"key":"146137_CR15","unstructured":"Rubio, J. E. (1986). Control and Optimisation: The Linear Treatment of Nonlinear Problems. MUP-Wiley."},{"key":"146137_CR16","unstructured":"Rubio, J. E. (1994). Optimization and Nonstandard Analysis. Marcel Dekker."},{"key":"146137_CR17","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1137\/0326013","volume":"26","author":"R. B. Vinter","year":"1988","unstructured":"Vinter, R. B. and Pereira, F. M. F. L. (1988). A maximum principle for optimal processes with discontinuous trajectories. SIAM Journal on Control and Optimization, 26: 205\u2013229.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"146137_CR18","unstructured":"Young, L. C. (1969). Calculus of Variations and Optimal Control Theory. W. B. Saunders."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1008213919383.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1008213919383\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1008213919383.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:40:37Z","timestamp":1751366437000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1008213919383"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,4]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,4]]}},"alternative-id":["146137"],"URL":"https:\/\/doi.org\/10.1023\/a:1008213919383","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[1998,4]]}}}