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Each subproblem is solved with a modified Newton method that generates search directions from a primal-dual system similar to that proposed for interior methods. The augmented penalty-barrier function may be interpreted as a merit function for values of the primal and dual variables.<\/jats:p>\n                  <jats:p>An inertia-controlling symmetric indefinite factorization is used to provide descent directions and directions of negative curvature for the augmented penalty-barrier merit function. A method suitable for large problems can be obtained by providing a version of this factorization that will treat large sparse indefinite systems.<\/jats:p>","DOI":"10.1137\/s1052623496305560","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1132-1152","source":"Crossref","is-referenced-by-count":107,"title":["Primal-Dual Interior Methods for Nonconvex Nonlinear Programming"],"prefix":"10.1137","volume":"8","author":[{"given":"Anders","family":"Forsgren","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Philip E.","family":"Gill","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","unstructured":"M. Arioli, T. F. Chan, I. S. Duff, N. I. M. Gould, and J. K. 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