{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T09:15:41Z","timestamp":1776849341218,"version":"3.51.2"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2007,11,20]],"date-time":"2007-11-20T00:00:00Z","timestamp":1195516800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2009,7]]},"DOI":"10.1007\/s10589-007-9147-4","type":"journal-article","created":{"date-parts":[[2007,11,19]],"date-time":"2007-11-19T14:46:04Z","timestamp":1195483564000},"page":"307-328","source":"Crossref","is-referenced-by-count":28,"title":["An inexact-restoration method for nonlinear bilevel programming problems"],"prefix":"10.1007","volume":"43","author":[{"given":"R.","family":"Andreani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. L. C.","family":"Castro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. L.","family":"Chela","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Friedlander","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. A.","family":"Santos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,11,20]]},"reference":[{"key":"9147_CR1","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s001860100158","volume":"54","author":"R. Andreani","year":"2001","unstructured":"Andreani, R., Mart\u00ednez, J.M.: On the solution of mathematical programming problems with equilibrium constraints. Math. Method. Oper. Res. 54, 345\u2013358 (2001)","journal-title":"Math. Method. Oper. Res."},{"key":"9147_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2836-1","volume-title":"Practical Bilevel Optimization: Algorithms and Applications","author":"J.F. Bard","year":"1998","unstructured":"Bard, J.F.: Practical Bilevel Optimization: Algorithms and Applications. Kluwer Academic, Dordrecht (1998)"},{"key":"9147_CR3","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1023\/A:1019928808826","volume":"23","author":"E.J. Birgin","year":"2002","unstructured":"Birgin, E.J., Mart\u00ednez, J.M.: Large-scale active-set box-constrained optimization method with spectral projected gradients. Comput. Optim. Appl. 23, 101\u2013125 (2002)","journal-title":"Comput. Optim. Appl."},{"key":"9147_CR4","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1287\/opre.21.1.37","volume":"21","author":"J. Bracken","year":"1973","unstructured":"Bracken, J., McGill, J.: Mathematical programs with optimization problems in the constraints. Oper. Res. 21, 37\u201344 (1973)","journal-title":"Oper. Res."},{"key":"9147_CR5","unstructured":"Candler, W., Norton, R.: Multilevel programming. Technical Report\u00a020, World Bank Development Research Center, Washington DC, USA"},{"key":"9147_CR6","unstructured":"Castro, S.L.C., Fancello, E.A., Friedlander, A., Santos, S.A.: Computational experiments in truss topology design with an inexact restoration method. Technical Report (2006), available at http:\/\/www.ime.unicamp.br\/~friedlan"},{"key":"9147_CR7","unstructured":"Colson, B.: BIPA (Bilevel programming with approximation methods): Software guide and test problems. Technical Report CRT-2002-38, Centre de Recherche sur les Transports, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, QC, Canada (2002)"},{"issue":"3","key":"9147_CR8","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s10589-005-4612-4","volume":"30","author":"B. Colson","year":"2005","unstructured":"Colson, B., Marcotte, P., Savard, G.: A trust-region method for nonlinear bilevel programming: Algorithm and computational experience. Comput. Optim. Appl. 30(3), 211\u2013227 (2005)","journal-title":"Comput. Optim. Appl."},{"key":"9147_CR9","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s10288-005-0071-0","volume":"3","author":"B. Colson","year":"2005","unstructured":"Colson, B., Marcotte, P., Savard, G.: Bilevel programming: A survey. 4OR: Q. J. Oper. Res. 3, 87\u2013107 (2005)","journal-title":"4OR: Q. J. Oper. Res."},{"issue":"3","key":"9147_CR10","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1137\/S1052623401383455","volume":"13","author":"Y. Dai","year":"2002","unstructured":"Dai, Y.: Convergence properties of the BFGS Algorithm. SIAM J. Optim. 13(3), 693\u2013701 (2002)","journal-title":"SIAM J. Optim."},{"key":"9147_CR11","series-title":"Nonconvex Optimization and its Applications Series","volume-title":"Foundations of Bilevel Programming","author":"S. Dempe","year":"2002","unstructured":"Dempe, S.: Foundations of Bilevel Programming. Nonconvex Optimization and its Applications Series, vol.\u00a061. Kluwer Academic, Dordrecht (2002)"},{"key":"9147_CR12","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1080\/0233193031000149894","volume":"52","author":"S. Dempe","year":"2003","unstructured":"Dempe, S.: Annottated bibliography on bilevel programming and mathematical problems with equilibrium constraints. Optimization 52, 333\u2013359 (2003)","journal-title":"Optimization"},{"key":"9147_CR13","unstructured":"Dempe, S.: Bilevel programming\u2014A survey. Technical Report TU 2003-11, Bergakademie Freiberg (2003)"},{"issue":"1","key":"9147_CR14","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1137\/S1052623496305882","volume":"9","author":"F. Facchinei","year":"1998","unstructured":"Facchinei, F., Fischer, A., Kanzow, C.: On the accurate identification of active constraints. SIAM J. Optim. 9(1), 14\u201332 (1998)","journal-title":"SIAM J. Optim."},{"key":"9147_CR15","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s10107990015a","volume":"85","author":"F. Facchinei","year":"1999","unstructured":"Facchinei, F., Jiang, H., Qi, L.: A smoothing method for mathematical programs with equilibrium constraints. Math. Program. 85, 107\u2013134 (1999)","journal-title":"Math. Program."},{"key":"9147_CR16","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1287\/moor.24.3.699","volume":"24","author":"A. Fischer","year":"1999","unstructured":"Fischer, A.: Modified Wilson method for nonlinear programs with nonunique multipliers. Math. Oper. Res. 24, 699\u2013727 (1999)","journal-title":"Math. Oper. Res."},{"issue":"1","key":"9147_CR17","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1137\/S1052623402407382","volume":"17","author":"R. Fletcher","year":"2006","unstructured":"Fletcher, R., Leyffer, S., Ralph, D., Scholtes, S.: Local convergence of SQP methods for mathematical programs with equilibrium constraints. SIAM J. Optim. 17(1), 259\u2013286 (2006)","journal-title":"SIAM J. Optim."},{"key":"9147_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3040-1","volume-title":"Handbook of Test Problems in Local and Global Optimization","author":"C.A. Floudas","year":"1999","unstructured":"Floudas, C.A., et al.: Handbook of Test Problems in Local and Global Optimization. Kluwer Academic, Dordrecht (1999)"},{"key":"9147_CR19","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s101070050051","volume":"85","author":"W.W. Hager","year":"1999","unstructured":"Hager, W.W., Gowda, M.S.: Stability in the presence of degeneracy and error estimation. Math. Program. 85, 181\u2013192 (1999)","journal-title":"Math. Program."},{"key":"9147_CR20","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511983658","volume-title":"Mathematical Programs with Equilibrium Constraints","author":"Z.Q. Luo","year":"1996","unstructured":"Luo, Z.Q., Pang, J.S., Ralph, D.: Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge (1996)"},{"issue":"2","key":"9147_CR21","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1023\/A:1022626332710","volume":"96","author":"J.M. Mart\u00ednez","year":"1998","unstructured":"Mart\u00ednez, J.M.: Two-phase model algorithm with global convergence for nonlinear programming. J.\u00a0Optim. Theory Appl. 96(2), 397\u2013436 (1998)","journal-title":"J.\u00a0Optim. Theory Appl."},{"issue":"1","key":"9147_CR22","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1023\/A:1017567113614","volume":"111","author":"J.M. Mart\u00ednez","year":"2001","unstructured":"Mart\u00ednez, J.M.: Inexact-restoration method with Lagrangian tangent decrease and new merit function for nonlinear programming. J.\u00a0Optim. Theory Appl. 111(1), 39\u201358 (2001)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9147_CR23","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1023\/A:1004632923654","volume":"104","author":"J.M. Mart\u00ednez","year":"2000","unstructured":"Mart\u00ednez, J.M., Pilotta, E.A.: Inexact-restoration algorithm for constrained optimization. J.\u00a0Optim. Theory Appl. 104, 135\u2013163 (2000)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9147_CR24","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/0-387-24255-4_12","volume-title":"Optimization and Control with Applications","author":"J.M. Mart\u00ednez","year":"2005","unstructured":"Mart\u00ednez, J.M., Pilotta, E.A.: Inexact restoration methods for nonlinear programming: Advances and perspectives. In: Qi, L.Q., Teo, K.L., Yang, X.Q. (eds.) Optimization and Control with Applications, pp.\u00a0271\u2013292. Springer, New York (2005)"},{"key":"9147_CR25","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1023\/A:1024791525441","volume":"118","author":"J.M. Mart\u00ednez","year":"2003","unstructured":"Mart\u00ednez, J.M., Svaiter, B.F.: A practical optimality condition without constraint qualifications for nonlinear programming. J.\u00a0Optim. Theory Appl. 118, 117\u2013133 (2003)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"9147_CR26","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/s10107-003-0421-7","volume":"99","author":"W.F. Mascarenhas","year":"2004","unstructured":"Mascarenhas, W.F.: The BFGS method with exact line searches fails for non-convex objective functions. Math. Program. Ser.\u00a0B 99, 49\u201361 (2004)","journal-title":"Math. Program. Ser.\u00a0B"},{"key":"9147_CR27","unstructured":"Murtagh, B.A., Saunders, M.A.: MINOS 5.4 User\u2019s Guide. Technical Report SOL 83-20, Stanford University (1995)"},{"key":"9147_CR28","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational Analysis","author":"R.T. Rockafellar","year":"1998","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational Analysis. Springer, Berlin (1998)"},{"key":"9147_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-6305-1","volume-title":"Nondifferentiable and Two-Level Mathematical Programming","author":"K. Shimizu","year":"1997","unstructured":"Shimizu, K., Ishizuka, Y., Bard, J.F.: Nondifferentiable and Two-Level Mathematical Programming. Kluwer Academic, Dordrecht (1997)"},{"issue":"3","key":"9147_CR30","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1137\/S0363012997317475","volume":"37","author":"M.V. Solodov","year":"1999","unstructured":"Solodov, M.V., Svaiter, B.F.: A new projection method for variational inequality problems. SIAM J. Control Optim. 37(3), 756\u2013776 (1999)","journal-title":"SIAM J. Control Optim."},{"key":"9147_CR31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01096458","volume":"5","author":"L.N. Vicente","year":"1994","unstructured":"Vicente, L.N., Calamai, P.H.: Bilevel and multilevel programming: A bibliography review. J. Global Optim. 5, 1\u201323 (1994)","journal-title":"J. Global Optim."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-007-9147-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-007-9147-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-007-9147-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:34Z","timestamp":1559302594000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-007-9147-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11,20]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,7]]}},"alternative-id":["9147"],"URL":"https:\/\/doi.org\/10.1007\/s10589-007-9147-4","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11,20]]}}}