{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T12:54:54Z","timestamp":1777467294575,"version":"3.51.4"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,12,18]],"date-time":"2018-12-18T00:00:00Z","timestamp":1545091200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2019,5]]},"DOI":"10.1007\/s10957-018-01461-z","type":"journal-article","created":{"date-parts":[[2018,12,18]],"date-time":"2018-12-18T05:14:44Z","timestamp":1545110084000},"page":"479-503","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Combination of Direct Methods and Homotopy in Numerical Optimal Control: Application to the Optimization of Chemotherapy in Cancer"],"prefix":"10.1007","volume":"181","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5119-9054","authenticated-orcid":false,"given":"Antoine","family":"Olivier","sequence":"first","affiliation":[]},{"given":"Camille","family":"Pouchol","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,12,18]]},"reference":[{"key":"1461_CR1","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1016\/j.matpur.2017.10.007","volume":"116","author":"C Pouchol","year":"2017","unstructured":"Pouchol, C., Clairambault, J., Lorz, A., Tr\u00e9lat, E.: Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy. Journal de Math\u00e9matiques Pures et Appliqu\u00e9es 116, 268\u2013308 (2017). https:\/\/doi.org\/10.1016\/j.matpur.2017.10.007","journal-title":"Journal de Math\u00e9matiques Pures et Appliqu\u00e9es"},{"key":"1461_CR2","doi-asserted-by":"crossref","unstructured":"Lorz, A., Lorenzi, T., Clairambault, J., Escargueil, A., Perthame, B.: Effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors. arXiv preprint arXiv:1312.6237 (2013)","DOI":"10.1007\/s11538-014-0046-4"},{"issue":"5","key":"1461_CR3","first-page":"519","volume":"36","author":"R Fourer","year":"2002","unstructured":"Fourer, R., Gay, D.M., Kernighan, B.W.: A modeling language for mathematical programming. Duxbury Press 36(5), 519\u2013554 (2002)","journal-title":"Duxbury Press"},{"issue":"1","key":"1461_CR4","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A W\u00e4chter","year":"2006","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25\u201357 (2006)","journal-title":"Math. Program."},{"issue":"3","key":"1461_CR5","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1007\/s10957-012-0050-5","volume":"154","author":"E Tr\u00e9lat","year":"2012","unstructured":"Tr\u00e9lat, E.: Optimal control and applications to aerospace: some results and challenges. J. Optim. Theory Appl. 154(3), 713\u2013758 (2012)","journal-title":"J. Optim. Theory Appl."},{"issue":"6","key":"1461_CR6","doi-asserted-by":"publisher","first-page":"654","DOI":"10.1002\/oca.1016","volume":"33","author":"M Cerf","year":"2012","unstructured":"Cerf, M., Haberkorn, T., Tr\u00e9lat, E.: Continuation from a flat to a round earth model in the coplanar orbit transfer problem. Optimal Control Appl. Methods 33(6), 654\u2013675 (2012)","journal-title":"Optimal Control Appl. Methods"},{"issue":"3","key":"1461_CR7","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1051\/m2an\/2016044","volume":"51","author":"M Chupin","year":"2017","unstructured":"Chupin, M., Haberkorn, T., Tr\u00e9lat, E.: Low-thrust Lyapunov to Lyapunov and Halo to Halo with $$L^2$$ L 2 -minimization. ESAIM: Math. Model. Numer. Anal. 51(3), 965\u2013996 (2017)","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"issue":"2","key":"1461_CR8","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1051\/cocv:2006003","volume":"12","author":"Joseph Gergaud","year":"2006","unstructured":"Gergaud, Joseph, Haberkorn, Thomas: Homotopy method for minimum consumption orbit transfer problem. ESAIM: COCV 12(2), 294\u2013310 (2006). https:\/\/doi.org\/10.1051\/cocv:2006003","journal-title":"ESAIM: COCV"},{"issue":"1","key":"1461_CR9","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s10569-012-9443-x","volume":"114","author":"JB Caillau","year":"2012","unstructured":"Caillau, J.B., Daoud, B., Gergaud, J.: Minimum fuel control of the planar circular restricted three-body problem. Celest. Mech. Dyn. Astron. 114(1), 137\u2013150 (2012). https:\/\/doi.org\/10.1007\/s10569-012-9443-x","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"1461_CR10","doi-asserted-by":"crossref","unstructured":"Bulirsch, R., Nerz, E., Pesch, H.J., von Stryk, O.: Combining direct and indirect methods in optimal control: range maximization of a hang glider. In: Bulirsch, R., Miele, A., Stoer, J., Well, K. (eds.) Optimal Control. ISNM International Series of Numerical Mathematics, vol. 111. Birkh\u00e4user, Basel (1993)","DOI":"10.1007\/978-3-0348-7539-4_20"},{"issue":"1","key":"1461_CR11","first-page":"2","volume":"23","author":"HJ Pesch","year":"1994","unstructured":"Pesch, H.J.: A practical guide to the solution of real-life optimal control problems. Control Cybern. 23(1), 2 (1994)","journal-title":"Control Cybern."},{"issue":"1","key":"1461_CR12","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/BF02071065","volume":"37","author":"O Stryk von","year":"1992","unstructured":"von Stryk, O., Bulirsch, R.: Direct and indirect methods for trajectory optimization. Ann. Oper. Res. 37(1), 357\u2013373 (1992). https:\/\/doi.org\/10.1007\/BF02071065","journal-title":"Ann. Oper. Res."},{"key":"1461_CR13","first-page":"47","volume":"63","author":"O Diekmann","year":"2004","unstructured":"Diekmann, O., et al.: A beginner\u2019s guide to adaptive dynamics. Banach Center Publ. 63, 47\u201386 (2004)","journal-title":"Banach Center Publ."},{"issue":"4","key":"1461_CR14","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.tpb.2004.12.003","volume":"67","author":"O Diekmann","year":"2005","unstructured":"Diekmann, O., Jabin, P.E., Mischler, S., Perthame, B.: The dynamics of adaptation: an illuminating example and a Hamilton\u2013Jacobi approach. Theor. Popul. Biol. 67(4), 257\u2013271 (2005)","journal-title":"Theor. Popul. Biol."},{"key":"1461_CR15","volume-title":"Transport Equations in Biology","author":"B Perthame","year":"2006","unstructured":"Perthame, B.: Transport Equations in Biology. Springer, New York (2006)"},{"issue":"11","key":"1461_CR16","doi-asserted-by":"publisher","first-page":"2627","DOI":"10.1016\/j.bbagen.2016.06.009","volume":"1860","author":"RH Chisholm","year":"2016","unstructured":"Chisholm, R.H., Lorenzi, T., Clairambault, J.: Cell population heterogeneity and evolution towards drug resistance in cancer: biological and mathematical assessment, theoretical treatment optimisation. Biochimica et Biophysica Acta (BBA) - General Subjects 1860(11), 2627\u20132645 (2016). https:\/\/doi.org\/10.1016\/j.bbagen.2016.06.009","journal-title":"Biochimica et Biophysica Acta (BBA) - General Subjects"},{"key":"1461_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-2972-6","volume-title":"Optimal Control for Mathematical Models of Cancer Therapies","author":"H Sch\u00e4ttler","year":"2015","unstructured":"Sch\u00e4ttler, H., Ledzewicz, U.: Optimal Control for Mathematical Models of Cancer Therapies. Springer, New York (2015). https:\/\/doi.org\/10.1007\/978-1-4939-2972-6"},{"issue":"3","key":"1461_CR18","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1093\/imammb\/9.3.215","volume":"9","author":"M Costa","year":"1992","unstructured":"Costa, M., Boldrini, J., Bassanezi, R.: Optimal chemical control of populations developing drug resistance. Math. Med. Biol. 9(3), 215\u2013226 (1992)","journal-title":"Math. Med. Biol."},{"key":"1461_CR19","first-page":"185","volume-title":"Tutorials in Mathematical Biosciences III. Lecture Notes in Mathematics","author":"M Kimmel","year":"2006","unstructured":"Kimmel, M., \u015awierniak, A.: Control theory approach to cancer chemotherapy: benefiting from phase dependence and overcoming drug resistance. In: Friedman, A. (ed.) Tutorials in Mathematical Biosciences III. Lecture Notes in Mathematics, vol. 1872, pp. 185\u2013221. Springer, Berlin (2006)"},{"issue":"1","key":"1461_CR20","doi-asserted-by":"crossref","first-page":"129","DOI":"10.3934\/dcdsb.2006.6.129","volume":"6","author":"U Ledzewicz","year":"2006","unstructured":"Ledzewicz, U., Sch\u00e4ttler, H.: Drug resistance in cancer chemotherapy as an optimal control problem. Discrete Contin. Dyn. Syst. Ser. B 6(1), 129 (2006)","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"issue":"02","key":"1461_CR21","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1142\/S0218339014400014","volume":"22","author":"U Ledzewicz","year":"2014","unstructured":"Ledzewicz, U., Sch\u00e4ttler, H.: On optimal chemotherapy for heterogeneous tumors. J. Biol. Syst. 22(02), 177\u2013197 (2014)","journal-title":"J. Biol. Syst."},{"key":"1461_CR22","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/j.jtbi.2016.11.009","volume":"413","author":"C Carr\u00e8re","year":"2017","unstructured":"Carr\u00e8re, C.: Optimization of an in vitro chemotherapy to avoid resistant tumours. J. Theor. Biol. 413, 24\u201333 (2017). https:\/\/doi.org\/10.1016\/j.jtbi.2016.11.009","journal-title":"J. Theor. Biol."},{"issue":"02","key":"1461_CR23","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1051\/m2an\/2012031","volume":"47","author":"A Lorz","year":"2013","unstructured":"Lorz, A., Lorenzi, T., Hochberg, M.E., Clairambault, J., Perthame, B.: Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies. ESAIM: Math. Model. Numer. Anal. 47(02), 377\u2013399 (2013)","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"issue":"3","key":"1461_CR24","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1007\/s11538-014-9936-8","volume":"76","author":"J Greene","year":"2014","unstructured":"Greene, J., Lavi, O., Gottesman, M.M., Levy, D.: The impact of cell density and mutations in a model of multidrug resistance in solid tumors. Bull. Math. Biol. 76(3), 627\u2013653 (2014)","journal-title":"Bull. Math. Biol."},{"key":"1461_CR25","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1016\/j.jtbi.2015.08.031","volume":"386","author":"T Lorenzi","year":"2015","unstructured":"Lorenzi, T., Chisholm, R.H., Desvillettes, L., Hughes, B.D.: Dissecting the dynamics of epigenetic changes in phenotype-structured populations exposed to fluctuating environments. J. Theor. Biol. 386, 166\u2013176 (2015)","journal-title":"J. Theor. Biol."},{"issue":"1","key":"1461_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11538-014-0046-4","volume":"77","author":"A Lorz","year":"2015","unstructured":"Lorz, A., Lorenzi, T., Clairambault, J., Escargueil, A., Perthame, B.: Modeling the effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors. Bull. Math. Biol. 77(1), 1\u201322 (2015)","journal-title":"Bull. Math. Biol."},{"key":"1461_CR27","volume-title":"Optimal Control Theory for Infinite Dimensional Systems","author":"X Li","year":"2012","unstructured":"Li, X., Yong, J.: Optimal Control Theory for Infinite Dimensional Systems. Springer, New York (2012)"},{"key":"1461_CR28","doi-asserted-by":"publisher","unstructured":"Leman, H., Meleard, S., Mirrahimi, S.: Influence of a spatial structure on the long time behavior of a competitive Lotka\u2013Volterra type system. Discrete Contin. Dyn. Syst. Ser. B (2014) https:\/\/doi.org\/10.1016\/j.matpur.2017.10.007","DOI":"10.1016\/j.matpur.2017.10.007"},{"key":"1461_CR29","unstructured":"Bonnefon, O., Coville, J., Legendre, G.: Concentration phenomenon in some non-local equation (2015). Preprint arXiv:1510.01971"},{"issue":"3","key":"1461_CR30","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1007\/s00220-013-1682-5","volume":"320","author":"X Cabr\u00e9","year":"2013","unstructured":"Cabr\u00e9, X., Roquejoffre, J.M.: The influence of fractional diffusion in fisher-KPP equations. Commun. Math. Phys. 320(3), 679\u2013722 (2013)","journal-title":"Commun. Math. Phys."},{"key":"1461_CR31","unstructured":"Coville, J.: Convergence to equilibrium for positive solutions of some mutation\u2013selection model (2013). Preprint arXiv:1308.6471"},{"issue":"4","key":"1461_CR32","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.4310\/CMS.2016.v14.n4.a16","volume":"14","author":"RH Chisholm","year":"2016","unstructured":"Chisholm, R.H., Lorenzi, T., Lorz, A.: Effects of an advection term in nonlocal Lotka\u2013Volterra equations. Commun. Math. Sci. 14(4), 1181\u20131188 (2016)","journal-title":"Commun. Math. Sci."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-018-01461-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-018-01461-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-018-01461-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T15:43:53Z","timestamp":1775317433000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-018-01461-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,18]]},"references-count":32,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["1461"],"URL":"https:\/\/doi.org\/10.1007\/s10957-018-01461-z","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,18]]},"assertion":[{"value":"26 July 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 December 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 December 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}