{"id":397,"date":"2021-03-15T14:41:19","date_gmt":"2021-03-15T18:41:19","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/hager\/?page_id=397"},"modified":"2026-03-19T08:18:26","modified_gmt":"2026-03-19T12:18:26","slug":"lpdasa-update-downdate","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/hager\/lpdasa-update-downdate\/","title":{"rendered":"LPDASA\/Update\/Downdate"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">LPDASA\/Update\/Downdate<\/h1>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager and H. Zhang,<\/a>\u00a0Projection onto a polyhedron that exploits sparsity, SIAM Journal on Optimization, 29 (2016), 1773-1798, doi:10.1137\/15M102825X<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">T. A. Davis and W. W. Hager,<\/a>\u00a0Dynamic supernodes in sparse Cholesky update\/downdate and triangular solves, ACM Transactions on Mathematical Software, 35 (2009)<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam,<\/a>\u00a0Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update\/downdate, ACM Transactions on Mathematical Software, 35 (2009).<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">T. A. Davis and W. W. Hager,<\/a>\u00a0Dual Multilevel Optimization, Mathematical Programming, 112 (2008), pp. 403-425.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">T. A. Davis and W. W. Hager,<\/a>\u00a0A sparse proximal implementation of the LP dual active set algorithm, Mathematical Programming, 112 (2008), pp. 275-301.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/objective-value-comparisons-for-netlib-test-problems\/\">Objective value comparisons for Netlib test problems<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">T. A. Davis and W. W. Hager,<\/a>\u00a0Row modifications of a sparse Cholesky factorization, SIAM Journal on Matrix Analysis and Applications, 26 (2005), pp. 621-639.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">T. A. Davis and W. W. Hager,<\/a>\u00a0Multiple-rank modifications of a sparse Cholesky factorization, SIAM Journal on Matrix Analysis and Applications, 22 (2001), pp. 997-1013.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">T. A. Davis and W. W. Hager,<\/a>\u00a0Modifying a Sparse Cholesky Factorization, SIAM Journal on Matrix Analysis and Applications, 20 (1999), pp. 606-627.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager,<\/a>\u00a0The dual active set algorithm and the iterative solution of linear programs, in Novel Approaches to Hard Discrete Optimization, P. M. Pardalos and H. Wolkowicz, Eds., Fields Institute Communications, Vol 37 (2003), 95-107.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager,<\/a>\u00a0The dual active set algorithm and its application to linear programming, Computational Optimization and Applications, 21 (2002), 263-275.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager<\/a>\u00a0The LP dual active set algorithm, High Performance Algorithms and Software in Nonlinear Optimization, R. De Leone, A. Murli, P. M. Pardalos, and G. Toraldo, eds., Kluwer, Dordrecht, 1998, pp. 243-254.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager, C.-L. Shih, and E. O. Lundin,<\/a>\u00a0Active set strategies and the LP dual active set algorithm<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager and D. W. Hearn,<\/a>\u00a0Application of the dual active set algorithm to quadratic network optimization, Computational Optimization and Applications, 1 (1993), 349-373.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager,<\/a>\u00a0The dual active set algorithm, in Advances in Optimization and Parallel Computing, P. M. Pardalos, ed., North Holland, Amsterdam, 1992, pp. 137-142.<\/li><\/ul>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":269,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-397","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/pages\/397","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/users\/269"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/comments?post=397"}],"version-history":[{"count":7,"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/pages\/397\/revisions"}],"predecessor-version":[{"id":821,"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/pages\/397\/revisions\/821"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/media?parent=397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}