{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:26:48Z","timestamp":1787336808118,"version":"3.56.0"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We present a general filter algorithm that allows a great deal of freedom in the step computation. Each iteration of the algorithm consists basically in computing a point which is not forbidden by the filter, from the current point. We prove its global convergence, assuming that the step must be efficient, in the sense that, near a feasible nonstationary point, the reduction of the objective function is \u201clarge.\u201d We show that this condition is reasonable, by presenting two classical ways of performing the step which satisfy it. In the first one, the step is obtained by the inexact restoration method of Mart\u00ednez and Pilotta. In the second, the step is computed by sequential quadratic programming.<\/jats:p>","DOI":"10.1137\/060672285","type":"journal-article","created":{"date-parts":[[2008,11,19]],"date-time":"2008-11-19T18:05:10Z","timestamp":1227117910000},"page":"1231-1249","source":"Crossref","is-referenced-by-count":28,"title":["Global Convergence of Filter Methods for Nonlinear Programming"],"prefix":"10.1137","volume":"19","author":[{"given":"Ademir A.","family":"Ribeiro","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elizabeth W.","family":"Karas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cl\u00f3vis C.","family":"Gonzaga","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,11,19]]},"reference":[{"key":"R1","unstructured":"D. P. Bertsekas,\n                      Nonlinear Programming\n                      , Athena Scientific, Belmont, MA, 1995."},{"key":"R2","unstructured":"R. H. Byrd,\n                      Robust Trust Region Methods for Constrained Optimization\n                      , Third SIAM Conference on Optimization, 1987."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/PL00011391"},{"key":"R4","unstructured":"C. M. Chin,\n                      A local convergence theory of a filter line search method for nonlinear programming\n                      , Technical report, Numerical Optimization Report, Department of Statistics, University of Oxford, England, January 2003."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-003-0378-6"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623499357258"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/s101070100244"},{"key":"R8","unstructured":"R. Fletcher, S. Leyffer, and P. L. Toint,\n                      On the global convergence of an SLP-filter algorithm\n                      , Technical Report NA\/183, Dept.  of Mathematics, Dundee University, 1998."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S105262340038081X"},{"key":"R10","first-page":"2","volume":"18","author":"Fletcher R.","year":"2007","journal-title":"SIAG\/Optimization Views-and-News"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"D. M. Gay, M. L. Overton, and M. H. Wright,\n                      A primal-dual interior method for nonconvex nonlinear programming\n                      , in Advances in Nonlinear Programming, Y. Y, ed., Kluwer Academic Publishers, Dordretch, 1998, pp. 31\u201356.","DOI":"10.1007\/978-1-4613-3335-7_2"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/s10107980014a"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623401399320"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623403422637"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/040603851"},{"key":"R16","unstructured":"N. I. M. Gould and P. L. Toint,\n                      The filter idea and its application to the nonlinear feasibility problem\n                      , in Proceedings of the 20th Biennal Conference on Numerical Analysis, D. F. Griffiths and G. A. Watson, eds., Scotland, 2003, pp. 73\u201379."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1145\/1206040.1206043"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-007-0123-7"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1023\/A:1017567113614"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004632923654"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024791525441"},{"key":"R22","unstructured":"E. Omojokun,\n                      Trust Region Algorithms for Optimization with Nonlinear Equality and Inequality Constraints\n                      , Ph.D. thesis, Dept. of Computer Science, University of Colorado, 1991."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/040603875"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-003-0477-4"},{"key":"R25","first-page":"217","volume":"100","author":"Ulbrich S.","year":"2004","journal-title":"Math. Program., Ser. B"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008677427361"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623403426544"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623403426556"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-004-0559-y"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060672285","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:31:37Z","timestamp":1787333497000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060672285"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/060672285"],"URL":"https:\/\/doi.org\/10.1137\/060672285","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}