{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:40:48Z","timestamp":1787341248183,"version":"build-2736575974"},"reference-count":27,"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":[[2014,1]]},"abstract":"<jats:p>We develop and analyze a trust-region sequential quadratic programming (SQP) method for the solution of smooth equality constrained optimization problems, which allows the inexact and hence iterative solution of linear systems. Iterative solution of linear systems is important in large-scale applications, such as optimization problems with partial differential equation constraints, where direct solves are either too expensive or not applicable. Our trust-region SQP algorithm is based on a composite-step approach that decouples the step into a quasi-normal and a tangential step. The algorithm includes critical modifications of substep computations needed to cope with the inexact solution of linear systems. The global convergence of our algorithm is guaranteed under rather general conditions on the substeps. We propose algorithms to compute the substeps and prove that these algorithms satisfy global convergence conditions. All components of the resulting algorithm are specified in such a way that they can be directly implemented. Numerical results indicate that our algorithm converges even for very coarse linear system solves.<\/jats:p>","DOI":"10.1137\/130921738","type":"journal-article","created":{"date-parts":[[2014,9,17]],"date-time":"2014-09-17T14:37:09Z","timestamp":1410964629000},"page":"1507-1541","source":"Crossref","is-referenced-by-count":52,"title":["A Matrix-Free Trust-Region SQP Method for Equality Constrained Optimization"],"prefix":"10.1137","volume":"24","author":[{"given":"Matthias","family":"Heinkenschloss","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Denis","family":"Ridzal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,9,11]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/0612048"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492904000212"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"G. Biros and O. Ghattas,\n                      Inexactness issues in the Lagrange-Newton-Krylov-Schur method for PDE-constrained optimization\n                      , in Large-Scale Constrained Optimization, L. T. Biegler, O. Ghattas, M. Heinkenschloss, and B. van Bloemen Waanders, eds., Lecture Notes in Comput. Sci. 30, Springer, Berlin, 2003, pp. 93-114.","DOI":"10.1007\/978-3-642-55508-4_6"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"\\AA. Bjo\u0308rck,\n                      Numerical Methods for Least Squares Problems\n                      , SIAM, Philadelphia, 1996.","DOI":"10.1137\/1.9781611971484"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-008-0248-3"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623497325107"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"A. R. Conn, N. I. M. Gould, and Ph. L. Toint,\n                      Trust-Region Methods\n                      , MPS\/SIAM Ser. Optim. 1, SIAM, Philadelphia, 2000.","DOI":"10.1137\/1.9780898719857"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623492238881"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/S036012995279031"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623494276026"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/080727129"},{"key":"atypb12","unstructured":"G. H. Golub and C. F. Van Loan,\n                      Matrix computations\n                      , 3rd ed., Johns Hopkins Stud. Math. Sci., Johns Hopkins University Press, Baltimore, MD, 1996."},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597323415"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598345667"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"M. Heinkenschloss and D. Ridzal,\n                      Integration of sequential quadratic programming and domain decomposition methods for nonlinear optimal control problems\n                      , in Domain Decomposition Methods in Science and EngineeringXVII, U. Langer, M. Discacciati, D. Keyes, O. Widlund, and W. Zulehner, eds., Lect. Notes Comput. Sci. Engrg. 60, Springer Verlag, Berlin, 2008, pp. 69-80.","DOI":"10.1007\/978-3-540-75199-1_6"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623499361543"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597325153"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1080\/10556789708805646"},{"key":"atypb19","doi-asserted-by":"crossref","unstructured":"J. Nocedal and S. J. Wright,\n                      Numerical Optimization\n                      , Springer Verlag, Berlin, 1999.","DOI":"10.1007\/b98874"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599362314"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/040602997"},{"key":"atypb22","unstructured":"D. Ridzal,\n                      Trust Region SQP Methods With Inexact Linear System Solves For Large-Scale Optimization\n                      , PhD thesis, Department of Computational and Applied Mathematics, Rice University, Houston, TX, 2006."},{"key":"atypb23","unstructured":"D. Ridzal, M. Aguilo\u0301, and M. Heinkenschloss,\n                      Numerical Study of a Matrix-Free Trust-Region SQP Method for Equality Constrained Optimization\n                      , Technical Report SAND 2011-9346, Sandia National Laboratories, Albuquerque, NM, 2011."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827502406415"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1137\/0720042"},{"key":"atypb26","first-page":"57","author":"Ph.","year":"1981","journal-title":"New York"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1137\/080743160"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130921738","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:11:15Z","timestamp":1787339475000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130921738"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1137\/130921738"],"URL":"https:\/\/doi.org\/10.1137\/130921738","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}