{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:27:06Z","timestamp":1787336826227,"version":"3.56.0"},"reference-count":7,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>In this short note we consider a sequential quadratic programming (SQP)--type method with conic subproblems and compare this method with a standard SQP method in which the conic constraint is linearized at each step. For both approaches we restrict our attention to convex subproblems since these are easy to solve and guarantee a certain global descent property. Using the example of a simple nonlinear program (NLP) and its conic reformulation we show that the SQP method with conic subproblems displays a slower rate of convergence than standard SQP methods. We then explain why an SQP subproblem that is based on a better approximation of the feasible set of the NLP results in a much slower algorithm.<\/jats:p>","DOI":"10.1137\/050625977","type":"journal-article","created":{"date-parts":[[2008,2,7]],"date-time":"2008-02-07T15:45:15Z","timestamp":1202399115000},"page":"1201-1210","source":"Crossref","is-referenced-by-count":12,"title":["Loss of Superlinear Convergence for an SQP-Type Method with Conic Constraints"],"prefix":"10.1137","volume":"16","author":[{"given":"Moritz","family":"Diehl","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Florian","family":"Jarre","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph H.","family":"Vogelbusch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623402417298"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900373483"},{"key":"R3","unstructured":"F. Jarre,\n                      On an Approximation of the Hessian of theLagrangian\n                      , http:\/\/www.optimization\u2010online.org\/ DB_HTML\/2003\/12\/800.html (2003)."},{"key":"R4","doi-asserted-by":"crossref","unstructured":"M.Powell, The convergence of variable metric methods for nonlinearly constrained optimization calculations, Academic Press, New York, 1978, 27\u20136380c:90138","DOI":"10.1016\/B978-0-12-468660-1.50007-4"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5610(96)00081-0"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1080\/10556789908805766"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-002-0347-5"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050625977","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:32:29Z","timestamp":1787333549000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050625977"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/050625977"],"URL":"https:\/\/doi.org\/10.1137\/050625977","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}