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Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an $\\epsilon$-feasible point and a second phase to seek optimality while maintaining at least $\\epsilon$-feasibility. Two-phase approaches of this kind based on a cubic regularization methodology have recently been proposed along with supporting worst-case iteration complexity analyses. Notably, in these approaches, the objective function is completely ignored in the first phase when $\\epsilon$-feasibility is sought. The main contribution of the method proposed in this paper is that the same worst-case iteration complexity is achieved, but with a first phase that also accounts for improvements in the objective function. As such, the method attempts to put significantly less burden on the second phase for seeking optimality.<\/jats:p>","DOI":"10.1137\/16m1108650","type":"journal-article","created":{"date-parts":[[2018,5,8]],"date-time":"2018-05-08T11:53:02Z","timestamp":1525780382000},"page":"1533-1563","source":"Crossref","is-referenced-by-count":8,"title":["Complexity Analysis of a Trust Funnel Algorithm for Equality Constrained Optimization"],"prefix":"10.1137","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7214-9187","authenticated-orcid":true,"given":"Frank E.","family":"Curtis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0251-4227","authenticated-orcid":true,"given":"Daniel P.","family":"Robinson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammadreza","family":"Samadi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,5,8]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"L. 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Toint,\n                      CUTEst: A Constrained and Unconstrained Testing Environment With Safe Threads\n                      , Technical report, RAL-TR-2013-005, Rutherford Appleton Laboratory, Didcot, 2013."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/080744542"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/080744554"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drq043"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-008-0244-7"},{"key":"atypb24","unstructured":"A. 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