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The method involves the computation of an approximate Newton direction for a primal-dual penalty-barrier function that incorporates shifts on both the primal and dual variables. Shifts on the dual variables allow the method to be safely \u201cwarm started\u201d from a good approximate solution and avoids the possibility of very large solutions of the associated path-following equations. The approximate Newton direction is used in conjunction with a new projected-search line-search algorithm that employs a flexible non-monotone quasi-Armijo line search for the minimization of each penalty-barrier function. Numerical results are presented for a large set of constrained optimization problems. For comparison purposes, results are also given for two primal-dual interior-point methods that do not use projection. The first is a method that shifts both the primal and dual variables. The second is a method that involves shifts on the primal variables only. The results show that the use of both primal and dual shifts in conjunction with projection gives a method that is more robust and requires significantly fewer iterations. In particular, the number of times that the search direction must be computed is substantially reduced. Results from a set of quadratic programming test problems indicate that the method is particularly well-suited to solving the quadratic programming subproblem in a sequential quadratic programming method for nonlinear optimization.<\/jats:p>","DOI":"10.1007\/s10589-023-00549-1","type":"journal-article","created":{"date-parts":[[2024,2,21]],"date-time":"2024-02-21T08:02:58Z","timestamp":1708502578000},"page":"37-70","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A projected-search interior-point method for nonlinearly constrained optimization"],"prefix":"10.1007","volume":"88","author":[{"given":"Philip E.","family":"Gill","sequence":"first","affiliation":[]},{"given":"Minxin","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,2,21]]},"reference":[{"key":"549_CR1","unstructured":"Gill, P.E., Zhang, M.: Equations for a projected-search path-following method for nonlinear optimization. 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