{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T15:00:02Z","timestamp":1776870002739,"version":"3.51.2"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T00:00:00Z","timestamp":1567987200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T00:00:00Z","timestamp":1567987200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["421386\/2016-9"],"award-info":[{"award-number":["421386\/2016-9"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["308523\/2017-2"],"award-info":[{"award-number":["308523\/2017-2"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2020,7]]},"DOI":"10.1007\/s10589-019-00129-2","type":"journal-article","created":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T14:02:40Z","timestamp":1568037760000},"page":"867-888","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Non-monotone inexact restoration method for nonlinear programming"],"prefix":"10.1007","volume":"76","author":[{"given":"Juliano B.","family":"Francisco","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8673-1319","authenticated-orcid":false,"given":"Douglas S.","family":"Gon\u00e7alves","sequence":"additional","affiliation":[]},{"given":"Ferm\u00edn S. V.","family":"Baz\u00e1n","sequence":"additional","affiliation":[]},{"given":"Lila L. T.","family":"Paredes","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,9]]},"reference":[{"issue":"3","key":"129_CR1","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s10589-007-9147-4","volume":"43","author":"R Andreani","year":"2009","unstructured":"Andreani, R., Castro, S.L.C., Chela, J.L., Friedlander, A., Santos, S.A.: An inexact-restoration method for nonlinear bilevel programming problems. Comput. Optim. Appl. 43(3), 307\u2013328 (2009)","journal-title":"Comput. Optim. Appl."},{"issue":"5","key":"129_CR2","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1080\/02331930903578700","volume":"60","author":"R Andreani","year":"2011","unstructured":"Andreani, R., Haeser, G., Mart\u00ednez, J.M.: On sequential optimality conditions for smooth constrained optimization. Optimization 60(5), 627\u2013641 (2011)","journal-title":"Optimization"},{"issue":"1","key":"129_CR3","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1137\/15M1008488","volume":"26","author":"R Andreani","year":"2016","unstructured":"Andreani, R., Mart\u00ednez, J.M., Ramos, A., Silva, P.J.S.: A cone-continuity constraint qualification and algorithmic consequences. SIAM J. Optim. 26(1), 96\u2013110 (2016)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"129_CR4","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1287\/moor.2017.0879","volume":"43","author":"R Andreani","year":"2018","unstructured":"Andreani, R., Mart\u00ednez, J.M., Ramos, A., Silva, P.J.S.: Strict constraint qualifications and sequential optimality conditions for constrained optimization. Math. Oper. Res. 43(3), 693\u2013717 (2018)","journal-title":"Math. Oper. Res."},{"issue":"15","key":"129_CR5","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.cam.2015.04.047","volume":"290","author":"B Aroux\u00e9t","year":"2015","unstructured":"Aroux\u00e9t, B., Echebest, N.E., Pilotta, E.A.: Inexact restoration method for nonlinear optimization without derivatives. J. Comput. Appl. Math. 290(15), 26\u201343 (2015)","journal-title":"J. Comput. Appl. Math."},{"key":"129_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cam.2014.12.031","volume":"282","author":"EG Birgin","year":"2015","unstructured":"Birgin, E.G., Bueno, L.F., Mart\u00ednez, J.M.: Assessing the reability of general-purpose inexact restoration methods. J. Comput. Appl. Math. 282, 1\u201316 (2015)","journal-title":"J. Comput. Appl. Math."},{"key":"129_CR7","doi-asserted-by":"publisher","first-page":"1307","DOI":"10.1090\/mcom\/3246","volume":"87","author":"EG Birgin","year":"2018","unstructured":"Birgin, E.G., Kreji\u0107, N., Mart\u00ednez, J.M.: On the employment of inexact restoration for the minimization of functions whose evaluation is subject to errors. Math. Comput 87, 1307\u20131326 (2018)","journal-title":"Math. Comput"},{"key":"129_CR8","doi-asserted-by":"publisher","unstructured":"Birgin, E.G., Kreji\u0107, N., Mart\u00ednez, J.M.: Iteration and evaluation complexity for the minimization of functions whose computation is intrinsically inexact. Math. Comput., to appear (2019) (\n                  https:\/\/doi.org\/10.1090\/mcom\/3445\n                  \n                )","DOI":"10.1090\/mcom\/3445"},{"key":"129_CR9","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s10957-005-6537-6","volume":"127","author":"EG Birgin","year":"2005","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Local convergence of an inexact-restoration method and numerical experiments. J. Optim. Theory Appl. 127, 229\u2013247 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"129_CR10","series-title":"Fundamental of algorithms","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611973365","volume-title":"Practical augmented Lagrangian methods for constrained optimization","author":"EG Birgin","year":"2014","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Practical augmented Lagrangian methods for constrained optimization. Fundamental of algorithms. SIAM, Philadelphia (2014)"},{"issue":"2","key":"129_CR11","doi-asserted-by":"publisher","first-page":"1189","DOI":"10.1137\/110856253","volume":"23","author":"LF Bueno","year":"2013","unstructured":"Bueno, L.F., Friedlander, A., Mart\u00ednez, J.M., Sobral, F.N.C.: Inexact restoration method for derivative-free optimization with smooth constraints. SIAM J. Optim. 23(2), 1189\u20131213 (2013)","journal-title":"SIAM J. Optim."},{"key":"129_CR12","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1007\/s10957-014-0572-0","volume":"165","author":"LF Bueno","year":"2015","unstructured":"Bueno, L.F., Haeser, G., Mart\u00ednez, J.M.: A flexible inexact restoration method for constrained optimization. J. Optim. Theory. Appl. 165, 188\u2013208 (2015)","journal-title":"J. Optim. Theory. Appl."},{"issue":"6","key":"129_CR13","doi-asserted-by":"publisher","first-page":"1315","DOI":"10.1007\/s11590-015-0928-x","volume":"10","author":"LF Bueno","year":"2016","unstructured":"Bueno, L.F., Haeser, G., Mart\u00ednez, J.M.: An inexact restoration approach to optimization problems with multiobjective constraints under weighted-sum scalarization. Optim Lett. 10(6), 1315\u20131325 (2016)","journal-title":"Optim Lett."},{"issue":"2","key":"129_CR14","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1023\/A:1013653923062","volume":"112","author":"YH Dai","year":"2002","unstructured":"Dai, Y.H.: On the nonmonotone line search. J. Optim. Theory. Appl. 112(2), 315\u2013330 (2002)","journal-title":"J. Optim. Theory. Appl."},{"key":"129_CR15","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201\u2013213 (2002)","journal-title":"Math. Program."},{"key":"129_CR16","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s10589-009-9267-0","volume":"46","author":"A Fischer","year":"2010","unstructured":"Fischer, A., Friedlander, A.: A new line search inexact restoration approach for nonlinear programming. Comput. Optim. Appl. 46, 333\u2013346 (2010)","journal-title":"Comput. Optim. Appl."},{"key":"129_CR17","unstructured":"Francisco, J.B., Gon\u00e7alves, D.S., Viloche-Baz\u00e1n, F.S., Paredes, L.L.T.: A non-monotone inexact restoration approach for minimization with orthogonality constraints (2018). \n                  http:\/\/www.optimization-online.org\/DB_FILE\/2018\/10\/6860.pdf"},{"key":"129_CR18","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1007\/s10589-010-9318-6","volume":"50","author":"JB Francisco","year":"2011","unstructured":"Francisco, J.B., Mart\u00ednez, J.M., Mart\u00ednez, L., Pisnitchenko, F.I.: Inexact restoration methods for minimization problems that arise in electronic structure calculations. Comput. Optim. Appl. 50, 555\u2013590 (2011)","journal-title":"Comput. Optim. Appl."},{"issue":"10","key":"129_CR19","doi-asserted-by":"publisher","first-page":"2717","DOI":"10.1016\/j.cam.2012.01.014","volume":"236","author":"JB Francisco","year":"2012","unstructured":"Francisco, J.B., Viloche-Baz\u00e1n, F.S.: Nonmonotone algorithm for minimization on closed sets with application to minimization on stiefel manifolds. J. Comput. Appl. Math. 236(10), 2717\u20132727 (2012)","journal-title":"J. Comput. Appl. Math."},{"key":"129_CR20","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.apnum.2016.09.018","volume":"112","author":"JB Francisco","year":"2017","unstructured":"Francisco, J.B., Viloche-Baz\u00e1n, F.S., Weber-Mendon\u00e7a, M.: Non-monotone algorithm for minimization on arbitrary domains with applications to large-scale orthogonal procrustes problem. Appl. Numer. Math. 112, 51\u201364 (2017)","journal-title":"Appl. Numer. Math."},{"issue":"1","key":"129_CR21","first-page":"109","volume":"30","author":"A Friedlander","year":"2011","unstructured":"Friedlander, A., Gomes, F.A.M.: Solution of a truss topology bilevel programming problem by means of an inexact restoration method. Comput. Appl. Math. 30(1), 109\u2013125 (2011)","journal-title":"Comput. Appl. Math."},{"key":"129_CR22","first-page":"489","volume":"163","author":"J Fu","year":"2005","unstructured":"Fu, J., Sun, W.: Nonmonotone adaptive trust-region method for unconstrained optimization problems. Appl. Math. Comput. 163, 489\u2013504 (2005)","journal-title":"Appl. Math. Comput."},{"key":"129_CR23","volume-title":"Matrix Computations","author":"GA Golub","year":"1996","unstructured":"Golub, G.A., van Loan, C.F.: Matrix Computations, 3rd edn. The John Hopkins University Press, London (1996)","edition":"3"},{"issue":"3","key":"129_CR24","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1137\/S1052623401399320","volume":"14","author":"CC Gonzaga","year":"2003","unstructured":"Gonzaga, C.C., Karas, E.W., Vanti, M.: A globally convergent filter method for nonlinear programming. SIAM J. Optim. 14(3), 646\u2013669 (2003)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"129_CR25","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1007\/s10107-014-0816-7","volume":"153","author":"B Jiang","year":"2015","unstructured":"Jiang, B., Dai, Y.H.: A framework of constraint preserving update schemes for optimization on Stiefel manifold. Math. Program. 153(2), 535\u2013575 (2015)","journal-title":"Math. Program."},{"key":"129_CR26","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/s10589-007-9162-5","volume":"44","author":"EW Karas","year":"2009","unstructured":"Karas, E.W., Pilotta, E., Ribeiro, A.: Numerical comparison of merit function with filter criterion in inexact restoration algorithms using hard-spheres problems. Comput. Optim. Appl. 44, 427\u2013441 (2009)","journal-title":"Comput. Optim. Appl."},{"issue":"4","key":"129_CR27","doi-asserted-by":"publisher","first-page":"1492","DOI":"10.1137\/090766668","volume":"48","author":"CY Kaya","year":"2010","unstructured":"Kaya, C.Y.: Inexact restoration for Runge\u2013Kutta discretization of optimal control problems. SIAM J. Numer. Anal. 48(4), 1492\u20131517 (2010)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"129_CR28","doi-asserted-by":"publisher","first-page":"1253","DOI":"10.1103\/RevModPhys.71.1253","volume":"71","author":"W Kohn","year":"1999","unstructured":"Kohn, W.: Nobel lecture: electronic structure of matter-wave functions and density functionals. Rev. Mod. Phys. 71(5), 1253\u20131266 (1999)","journal-title":"Rev. Mod. Phys."},{"key":"129_CR29","doi-asserted-by":"publisher","first-page":"1775","DOI":"10.1090\/mcom\/3025","volume":"85","author":"N Kreji\u0107","year":"2016","unstructured":"Kreji\u0107, N., Mart\u00ednez, J.M.: Inexact restoration approach for minimization with inexact evaluation of the objective function. Math. Comput. 85, 1775\u20131791 (2016)","journal-title":"Math. Comput."},{"issue":"3","key":"129_CR30","first-page":"73","volume":"8","author":"LS Lasdon","year":"1974","unstructured":"Lasdon, L.S., Fox, R.L., Ratner, M.W.: Nonlinear optimization using the generalized reduced gradient method. R.A.I.R.O. Oper. Res. 8(3), 73\u2013103 (1974)","journal-title":"R.A.I.R.O. Oper. Res."},{"key":"129_CR31","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1023\/A:1017567113614","volume":"111","author":"JM Mart\u00ednez","year":"2001","unstructured":"Mart\u00ednez, J.M.: Inexact restoration method with Lagrangian tangent decrease and new merit function for nonlinear programming. J. Optim. Theory. Appl. 111, 39\u201358 (2001)","journal-title":"J. Optim. Theory. Appl."},{"key":"129_CR32","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1023\/A:1004632923654","volume":"104","author":"JM Mart\u00ednez","year":"2000","unstructured":"Mart\u00ednez, J.M., Pilotta, E.A.: Inexact restoration algorithms for constrained optimization. J. Optim. Theory. Appl. 104, 135\u2013163 (2000)","journal-title":"J. Optim. Theory. Appl."},{"issue":"4","key":"129_CR33","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/BF00927947","volume":"4","author":"A Miele","year":"1969","unstructured":"Miele, A., Huang, H.Y., Heideman, J.C.: Sequential gradient-restoration algorithm for the minimization of constrained functions \u2014 ordinary and conjugate gradient versions. J. Optim. Theory. Appl. 4(4), 213\u2013243 (1969)","journal-title":"J. Optim. Theory. Appl."},{"issue":"2","key":"129_CR34","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1016\/j.imavis.2011.09.005","volume":"30","author":"S Mittal","year":"2012","unstructured":"Mittal, S., Meer, P.: Conjugate gradient on Grassmann manifolds for robust subspace estimation. Image. Vis. Comput. 30(2), 417\u2013427 (2012)","journal-title":"Image. Vis. Comput."},{"key":"129_CR35","first-page":"1412","volume":"25","author":"T Ngo","year":"2012","unstructured":"Ngo, T., Saad, Y.: Scaled gradients on Grassmann manifolds for matrix completion. Adv. Neural. Inf. Process. Syst. 25, 1412\u20131420 (2012)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"129_CR36","series-title":"Springer Series in Operations Research","doi-asserted-by":"publisher","DOI":"10.1007\/b98874","volume-title":"Numerical Optimization","author":"J Nocedal","year":"1999","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization. Springer Series in Operations Research. Springer, New York (1999)"},{"key":"129_CR37","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1137\/S1052623494266365","volume":"7","author":"M Raydan","year":"1997","unstructured":"Raydan, M.: The Barzilai and Borwein gradient method for large scale unconstrained minimization problem. SIAM J. Optim. 7, 26\u201333 (1997)","journal-title":"SIAM J. Optim."},{"key":"129_CR38","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1137\/S106482759427021X","volume":"17","author":"PL Toint","year":"1996","unstructured":"Toint, P.L.: An assessment of non-monotone linesearch techniques for unconstrained optimization. SIAM J. Sci. Comput. 17, 725\u2013739 (1996)","journal-title":"SIAM J. Sci. Comput."},{"key":"129_CR39","first-page":"69","volume":"77","author":"PL Toint","year":"1997","unstructured":"Toint, P.L.: Non-monotone trust region algorithm for nonlinear optimization subject to convex constraints. Math. Program. 77, 69\u201394 (1997)","journal-title":"Math. Program."},{"issue":"1","key":"129_CR40","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/s10107-012-0584-1","volume":"142","author":"Z Wen","year":"2013","unstructured":"Wen, Z., Yin, W.: A feasible method for optimization with orthogonality constraints. Math. Program. 142(1), 397\u2013434 (2013)","journal-title":"Math. Program."},{"issue":"4","key":"129_CR41","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1137\/S1052623403428208","volume":"14","author":"H Zhang","year":"2004","unstructured":"Zhang, H., Hager, W.: A nonmonotone line search technique and its application to unconstrained optimization. SIAM J. Optim. 14(4), 1043\u20131056 (2004)","journal-title":"SIAM J. Optim."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-019-00129-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-019-00129-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-019-00129-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,7]],"date-time":"2020-09-07T23:14:57Z","timestamp":1599520497000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-019-00129-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,9]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["129"],"URL":"https:\/\/doi.org\/10.1007\/s10589-019-00129-2","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,9,9]]},"assertion":[{"value":"15 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2019","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}