{"id":16538,"date":"2023-01-04T09:03:42","date_gmt":"2023-01-04T01:03:42","guid":{"rendered":"https:\/\/iora.nus.edu.sg\/?post_type=paper-p&#038;p=16538"},"modified":"2023-01-04T09:43:14","modified_gmt":"2023-01-04T01:43:14","slug":"qppal-a-two-phase-proximal-augmented-lagrangian-method-for-high-dimensional-convex-quadratic-programming-problems","status":"publish","type":"paper-p","link":"https:\/\/iora.nus.edu.sg\/paper-p\/qppal-a-two-phase-proximal-augmented-lagrangian-method-for-high-dimensional-convex-quadratic-programming-problems\/","title":{"rendered":"QPPAL: A two-phase proximal augmented Lagrangian method for high dimensional convex quadratic programming problems"},"content":{"rendered":"<p>In this paper, we aim to solve high dimensional convex quadratic programming (QP) problems with a large number of quadratic terms, linear equality and inequality constraints. In order to solve the targeted {\\bf QP} problems to a desired accuracy efficiently, we develop a two-phase {\\bf P}roximal {\\bf A}ugmented {\\bf L}agrangian method {(QPPAL)}, with Phase I to generate a reasonably good initial point to warm start Phase II to obtain an accurate solution efficiently. More specifically, in Phase I, based on the recently developed symmetric Gauss-Seidel (sGS) decomposition technique, we design a novel sGS based semi-proximal augmented Lagrangian method for the purpose of finding a solution of low to medium accuracy. Then, in Phase II, a proximal augmented Lagrangian algorithm is proposed to obtain a more accurate solution efficiently. Extensive numerical results evaluating the performance of {QPPAL} against {existing state-of-the-art solvers Gurobi, OSQP and QPALM} are presented to demonstrate the high efficiency and robustness of our proposed algorithm for solving various classes of large-scale convex QP problems. {The MATLAB implementation of the software package QPPAL is available at: https:\/\/blog.nus.edu.sg\/mattohkc\/softwares\/qppal\/<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this paper, we aim to solve high dimensional convex quadratic programming (QP) problems with a large number of quadratic terms, linear equality and inequality constraints. In order to solve [&hellip;]<\/p>\n","protected":false},"featured_media":16539,"template":"","meta":{"_acf_changed":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false},"tags":[],"publication":[78,77,50],"keyword":[],"class_list":["post-16538","paper-p","type-paper-p","status-publish","has-post-thumbnail","hentry","publication-moe-t3","publication-papers","publication-publications-by-iora"],"acf":[],"_links":{"self":[{"href":"https:\/\/iora.nus.edu.sg\/wp-json\/wp\/v2\/paper-p\/16538","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/iora.nus.edu.sg\/wp-json\/wp\/v2\/paper-p"}],"about":[{"href":"https:\/\/iora.nus.edu.sg\/wp-json\/wp\/v2\/types\/paper-p"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iora.nus.edu.sg\/wp-json\/wp\/v2\/media\/16539"}],"wp:attachment":[{"href":"https:\/\/iora.nus.edu.sg\/wp-json\/wp\/v2\/media?parent=16538"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iora.nus.edu.sg\/wp-json\/wp\/v2\/tags?post=16538"},{"taxonomy":"publication","embeddable":true,"href":"https:\/\/iora.nus.edu.sg\/wp-json\/wp\/v2\/publication?post=16538"},{"taxonomy":"keyword","embeddable":true,"href":"https:\/\/iora.nus.edu.sg\/wp-json\/wp\/v2\/keyword?post=16538"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}