{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:51:41Z","timestamp":1773233501839,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2010,4,3]],"date-time":"2010-04-03T00:00:00Z","timestamp":1270252800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2011,2]]},"DOI":"10.1007\/s11590-010-0189-7","type":"journal-article","created":{"date-parts":[[2010,4,2]],"date-time":"2010-04-02T01:48:06Z","timestamp":1270172886000},"page":"41-53","source":"Crossref","is-referenced-by-count":57,"title":["Transversality conditions for infinite horizon variational problems on time scales"],"prefix":"10.1007","volume":"5","author":[{"given":"Agnieszka B.","family":"Malinowska","sequence":"first","affiliation":[]},{"given":"Nat\u00e1lia","family":"Martins","sequence":"additional","affiliation":[]},{"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,4,3]]},"reference":[{"issue":"6","key":"189_CR1","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1177\/1077546309103268","volume":"15","author":"R. Almeida","year":"2009","unstructured":"Almeida R., Torres D.F.M.: Isoperimetric problems on time scales with nabla derivatives. J. Vib. Control 15(6), 951\u2013958 (2009)","journal-title":"J. Vib. Control"},{"issue":"7\u20138","key":"189_CR2","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1016\/j.mcm.2005.08.014","volume":"43","author":"F.M. Atici","year":"2006","unstructured":"Atici F.M., Biles D.C., Lebedinsky A.: An application of time scales to economics. Math. Comput. Modelling 43(7\u20138), 718\u2013726 (2006)","journal-title":"Math. Comput. Modelling"},{"issue":"1","key":"189_CR3","first-page":"1","volume":"9","author":"F.M. Atici","year":"2009","unstructured":"Atici F.M., McMahan C.S.: A comparison in the theory of calculus of variations on time scales with an application to the Ramsey model. Nonlinear Dyn. Syst. Theory 9(1), 1\u201310 (2009)","journal-title":"Nonlinear Dyn. Syst. Theory"},{"issue":"3","key":"189_CR4","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.aml.2007.03.013","volume":"21","author":"F.M. Atici","year":"2008","unstructured":"Atici F.M., Uysal F.: A production-inventory model of HMMS on time scales. Appl. Math. Lett. 21(3), 236\u2013243 (2008)","journal-title":"Appl. Math. Lett."},{"issue":"2","key":"189_CR5","doi-asserted-by":"crossref","first-page":"1220","DOI":"10.1016\/j.jmaa.2008.01.018","volume":"342","author":"Z. Bartosiewicz","year":"2008","unstructured":"Bartosiewicz Z., Torres D.F.M.: Noether\u2019s theorem on time scales. J. Math. Anal. Appl. 342(2), 1220\u20131226 (2008)","journal-title":"J. Math. Anal. Appl."},{"key":"189_CR6","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511559402","volume-title":"Optimization and stability theory for economic analysis","author":"B. Beavis","year":"1990","unstructured":"Beavis B., Dobbs I.M.: Optimization and stability theory for economic analysis. Cambridge University Press, Cambridge (1990)"},{"issue":"3\u20134","key":"189_CR7","first-page":"339","volume":"13","author":"M. Bohner","year":"2004","unstructured":"Bohner M.: Calculus of variations on time scales. Dyn. Syst. Appl. 13(3\u20134), 339\u2013349 (2004)","journal-title":"Dyn. Syst. Appl."},{"key":"189_CR8","doi-asserted-by":"crossref","unstructured":"Bohner, M., Ferreira, R.A.C., Torres, D.F.M.: Integral inequalities and their applications to the calculus of variations on time scales. Math. Inequal. Appl. (2010, in press)","DOI":"10.7153\/mia-13-35"},{"issue":"1\u20132","key":"189_CR9","first-page":"45","volume":"12","author":"M. Bohner","year":"2003","unstructured":"Bohner M., Guseinov G.Sh.: Improper integrals on time scales. Dyn. Syst. Appl. 12(1\u20132), 45\u201365 (2003)","journal-title":"Dyn. Syst. Appl."},{"key":"189_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0201-1","volume-title":"Dynamic Equations on Time Scales","author":"M. Bohner","year":"2001","unstructured":"Bohner M., Peterson A.: Dynamic Equations on Time Scales. Birkh\u00e4user, Boston (2001)"},{"key":"189_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-8176-8230-9","volume-title":"Advances in Dynamic Equations on Time Scales","author":"M. Bohner","year":"2003","unstructured":"Bohner M., Peterson A.: Advances in Dynamic Equations on Time Scales. Birkh\u00e4user, Boston (2003)"},{"key":"189_CR12","doi-asserted-by":"crossref","first-page":"275","DOI":"10.2307\/2296419","volume":"37","author":"W.A. Brock","year":"1970","unstructured":"Brock W.A.: On existence of weakly maximal programmes in a multi-sector economy. Rev. Econ. Stud. 37, 275\u2013280 (1970)","journal-title":"Rev. Econ. Stud."},{"key":"189_CR13","unstructured":"Cai, D., Nitta, T.G.: Treating the future equally: solving undiscounted infinite horizon optimization problems (2007) arXiv:math\/0701371v4 [math.OC]"},{"key":"189_CR14","unstructured":"Cai, D., Nitta, T.G.: Constructing the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems (2008) arXiv:0803.4046v1 [q-fin.GN]"},{"issue":"12","key":"189_CR15","doi-asserted-by":"crossref","first-page":"e2103","DOI":"10.1016\/j.na.2009.03.066","volume":"71","author":"D. Cai","year":"2009","unstructured":"Cai D., Nitta T.G.: Optimal solutions to the infinite horizon problems: Constructing the optimum as the limit of the solutions for the finite horizon problems. Nonlinear Anal. 71(12), e2103\u2013e2108 (2009)","journal-title":"Nonlinear Anal."},{"key":"189_CR16","volume-title":"Elements of Dynamic Optimization","author":"A.C. Chiang","year":"1992","unstructured":"Chiang A.C.: Elements of Dynamic Optimization. McGraw-Hill, Singapore (1992)"},{"key":"189_CR17","volume-title":"Economic Theory and Exhaustible Resources","author":"P.S. Dasgupta","year":"1979","unstructured":"Dasgupta P.S., Heal G.M.: Economic Theory and Exhaustible Resources. James Nisbet and Cambridge University Press, Cambridge (1979)"},{"key":"189_CR18","doi-asserted-by":"crossref","unstructured":"Ferreira, R.A.C., Torres, D.F.M.: Higher-order calculus of variations on time scales. In: Mathematical Control Theory and Finance, pp. 149\u2013159. Springer, Berlin (2008)","DOI":"10.1007\/978-3-540-69532-5_9"},{"key":"189_CR19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2296567","volume":"34","author":"D. Gale","year":"1967","unstructured":"Gale D.: On optimal development in a multisector economy. Rev. Econom. Stud. 34, 1\u201319 (1967)","journal-title":"Rev. Econom. Stud."},{"key":"189_CR20","volume-title":"Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Methods","author":"F. Giannessi","year":"2001","unstructured":"Giannessi F., Maugeri A., Pardalos P.M.: Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Methods. Kluwer, Dordrecht (2001)"},{"issue":"4","key":"189_CR21","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1111\/1468-0262.00227","volume":"69","author":"T. Kamihigashi","year":"2001","unstructured":"Kamihigashi T.: Necessity of transversality conditions for infinite horizon problems. Econometrica 69(4), 995\u20131012 (2001)","journal-title":"Econometrica"},{"issue":"2","key":"189_CR22","first-page":"77","volume":"24","author":"D. Kravvaritis","year":"1993","unstructured":"Kravvaritis D., Pantelides G., Papageorgiou N.S.: Optimal programs for a continuous time infinite horizon growth model. Indian J. Pure Appl. Math. 24(2), 77\u201386 (1993)","journal-title":"Indian J. Pure Appl. Math."},{"key":"189_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2698-5","volume-title":"Undergraduate Analysis","author":"S. Lang","year":"1997","unstructured":"Lang S.: Undergraduate Analysis, 2nd edn. Springer, New York (1997)","edition":"2"},{"key":"189_CR24","first-page":"469","volume":"18","author":"A.B. Malinowska","year":"2009","unstructured":"Malinowska A.B., Torres D.F.M.: On the diamond-alpha Riemann integral and mean value theorems on time scales. Dyn. Syst. Appl. 18, 469\u2013482 (2009)","journal-title":"Dyn. Syst. Appl."},{"key":"189_CR25","doi-asserted-by":"crossref","unstructured":"Malinowska, A.B., Torres, D.F.M.: Natural boundary conditions in the calculus of variations. Math. Methods Appl. Sci. (2010, in press). doi: 10.1002\/mma.1289","DOI":"10.1002\/mma.1289"},{"key":"189_CR26","doi-asserted-by":"crossref","unstructured":"Malinowska, A.B., Torres, D.F.M.: Leitmann\u2019s direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales. Appl. Math. Comput. (2010, in press). doi: 10.1016\/j.amc.2010.01.015","DOI":"10.1016\/j.amc.2010.01.015"},{"issue":"12","key":"189_CR27","doi-asserted-by":"crossref","first-page":"e763","DOI":"10.1016\/j.na.2008.11.035","volume":"71","author":"N. Martins","year":"2009","unstructured":"Martins N., Torres D.F.M.: Calculus of variations on time scales with nabla derivatives. Nonlinear Anal. 71(12), e763\u2013e773 (2009)","journal-title":"Nonlinear Anal."},{"issue":"3","key":"189_CR28","doi-asserted-by":"crossref","first-page":"705","DOI":"10.2307\/2938197","volume":"58","author":"P. Michel","year":"1990","unstructured":"Michel P.: Some clarifications on the transversality condition. Econometrica 58(3), 705\u2013723 (1990)","journal-title":"Econometrica"},{"issue":"12","key":"189_CR29","doi-asserted-by":"crossref","first-page":"1980","DOI":"10.1016\/j.na.2009.02.110","volume":"71","author":"R. Okomura","year":"2009","unstructured":"Okomura R., Cai D., Nitta T.G.: Transversality conditions for infinite horizon optimality: higher order differential problems. Nonlinear Anal. 71(12), 1980\u20131984 (2009)","journal-title":"Nonlinear Anal."},{"key":"189_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-0158-3","volume-title":"Nonlinear Analysis and Variational Problems","author":"P.M. Pardalos","year":"2010","unstructured":"Pardalos P.M., Rassias T.M., Khan A.A.: Nonlinear Analysis and Variational Problems. Springer, Berlin (2010)"},{"key":"189_CR31","doi-asserted-by":"crossref","first-page":"543","DOI":"10.2307\/2224098","volume":"38","author":"F. Ramsey","year":"1928","unstructured":"Ramsey F.: A mathematical theory of savings. Econ. J. 38, 543\u2013559 (1928)","journal-title":"Econ. J."},{"issue":"1","key":"189_CR32","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1155\/IJMMS.2005.57","volume":"2005","author":"I.E. Schochetman","year":"2005","unstructured":"Schochetman I.E., Smith R.L.: Optimality criteria for deterministic discrete-time infinite horizon optimization. Int. J. Math. Math. Sci. 2005(1), 57\u201380 (2005)","journal-title":"Int. J. Math. Math. Sci."},{"key":"189_CR33","doi-asserted-by":"crossref","first-page":"85","DOI":"10.2307\/2296054","volume":"32","author":"C.C. Von Weiszacker","year":"1965","unstructured":"Von Weiszacker C.C.: Existence of optimal programs of accumulation for an infinite time horizon. Rev. Econom. Stud. 32, 85\u2013104 (1965)","journal-title":"Rev. Econom. Stud."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-010-0189-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-010-0189-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-010-0189-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,3]],"date-time":"2019-06-03T11:15:04Z","timestamp":1559560504000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-010-0189-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,4,3]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,2]]}},"alternative-id":["189"],"URL":"https:\/\/doi.org\/10.1007\/s11590-010-0189-7","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,4,3]]}}}