{"id":485,"date":"2021-03-15T15:36:48","date_gmt":"2021-03-15T19:36:48","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/hager\/?page_id=485"},"modified":"2026-03-19T08:18:25","modified_gmt":"2026-03-19T12:18:25","slug":"gradient-methods-and-software","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/hager\/gradient-methods-and-software\/","title":{"rendered":"Gradient Methods and Software"},"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\">Gradient Methods and Software<\/h1>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/software\/\">Software<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">Daniela di Serafino, William W. Hager, Gerardo Toraldo, and Marco Viola,<\/a>\u00a0On the stationarity for nonlinear optimization problems with polyhedral constraints, Mathematical Programming, (2023), https:\/\/doi.org\/10.1007\/s10107-023-01979-9\/<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">William W. Hager and Hongchao Zhang,<\/a>\u00a0Algorithm 1035: A Gradient-Based Implementation of the Polyhedral Active Set Algorithm,\u00a0ACM Transactions on Mathematical Software, 49 (2023), No. 2, Article 20, 1-13, https:\/\/doi.org\/10.1145\/3583559<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">William W. Hager and Hongchao Zhang,<\/a>\u00a0An Active Set Algorithm for Nonlinear Optimization with Polyhedral Constraints,\u00a0Science China Mathematics, ICIAM Special Issue, 59 (2016), pp. 1525-1542, doi: 10.1007\/s11425-016-0300-6<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">William W. Hager and Hongchao 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\/\">William W. Hager and Hongchao Zhang,<\/a>\u00a0Projection onto a Polyhedron that Exploits Sparsity, paper plus data.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">Timothy A. Davis, William W. Hager, and James T. Hungerford,<\/a>\u00a0An Efficient Hybrid Algorithm for the Separable Convex Quadratic Knapsack Problem,\u00a0ACM TOMS, Vol 42 (2016), No. 3, Article 22.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">William W. Hager and Hongchao Zhang,<\/a>\u00a0The Limited Memory Conjugate Gradient Method,\u00a0SIAM Journal on Optimization, 23 (2013), pp. 2150-2168.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/performance-data-for-cg_descent-6-0\/\">Performance data for CG_DESCENT 6.0.<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">William W. Hager and Hongchao Zhang,<\/a>\u00a0An Affine Scaling Method for Optimization Problems with Polyhedral Constraints, Computational Optimization and Application, 59 (2014), pp. 163-183,\u00a0DOI 10.1007\/s10589-013-9535-x<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/an-affine-scaling-interior-point-method\/\">Maria D. Gonzalez-Lima, William W. Hager, and Hongchao Zhang,<\/a>\u00a0An Affine-scaling Interior-point Method for Continuous Knapsack Constraints with Application to Support Vector Machines, SIAM Journal on Optimization, 21 (2011), pp. 361-390.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/positron-emission-tomography-pet\/\">W. W. Hager, B. A. Mair, and H. Zhang,<\/a>\u00a0An Affine-scaling Interior-point CBB Method for Box-Constrained Optimization, Mathematical Programming, 119 (2009), pp. 1-32.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager and H. Zhang,<\/a>\u00a0A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM Journal on Optimization, 16 (2005), 170-192.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/performance-data-for-siopt-paper\/\">Performance data for SIOPT paper.<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager and H. Zhang,<\/a>\u00a0Algorithm 851: CG_DESCENT, A conjugate gradient method with guaranteed descent, ACM Transactions on Mathematical Software, 32 (2006), 113-137.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/performance-data-for-acm-toms-paper\/\">Performance data for ACM TOMS paper.<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager and H. Zhang,<\/a>\u00a0A survey of nonlinear conjugate gradient methods, Pacific Journal of Optimization, 2 (2006), pp. 35-58.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">Y-H. Dai, W. W. Hager, K. Schittkowski, and H. Zhang,<\/a>\u00a0The cyclic Barzilai-Borwein method for unconstrained optimization, IMA Journal on Numerical Analysis, 26 (2006), pp. 604 &#8211; 627.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager and H. Zhang,<\/a>\u00a0A new active set algorithm for box constrained optimization, SIAM Journal on Optimization, 17 (2006), pp. 526-557.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/performance-data-for-active-set-paper\/\">Performance data for active set paper.<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager and H. Zhang,<\/a>\u00a0Recent advances in bound constrained optimization, in System Modeling and Optimization, F. Ceragioli, A. Dontchev, H. Furuta, K. Marti, and L. Pandolfi, eds., Springer, 2006, pp. 67-82. (22nd IFIP TC 7 Conference on System Modeling and Optimization, Turin, Italy, July 18-22, 2005).<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">H. Zhang and W. W. Hager,<\/a>\u00a0A nonmonotone line search technique and its application to unconstrained optimization, SIAM Journal on Optimization, 14 (2004), pp. 1043-1056.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager and S. C. Park,<\/a>\u00a0The gradient projection method with exact line search, Journal of Global Optimization, 30 (2004), pp. 103-118.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager,<\/a>\u00a0Analysis and implementation of a dual algorithm for constrained optimization, Journal of Optimization Theory and Applications, 79 (1993), pp. 427-462.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager,<\/a>\u00a0A derivative-based bracketing scheme for univariate minimization and the conjugate gradient method, Computers Math. Applic., 18 (1989), pp. 779-795.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">N. Ghosh and W. W. Hager,<\/a>\u00a0A derivative-free bracketing scheme for univariate minimization, Computers Math. Applic., 20 (1990), pp. 23-34.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">Holly Peters Hirst,<\/a>\u00a0N-step quadratic convergence in the conjugate gradient method (Phd thesis at Penn State University, 1989)<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/content-removed\/\">W. W. Hager,<\/a> Dual techniques for constrained optimization, Journal of Optimization Theory and Applications, 55 (1987), pp. 37-71.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/hager\/gnu-general-public-license\/\">GNU GENERAL PUBLIC LICENSE<\/a><\/li><\/ul>\n\n\n\n\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-485","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/pages\/485","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=485"}],"version-history":[{"count":11,"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/pages\/485\/revisions"}],"predecessor-version":[{"id":814,"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/pages\/485\/revisions\/814"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/hager\/wp-json\/wp\/v2\/media?parent=485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}