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While Branch-and-Bound (BnB) frameworks can certify optimality using perspective relaxations, existing methods for solving these relaxations are computationally intensive, limiting their scalability. To address this challenge, we propose a unified proximal first-order algorithmic framework that is both linearly convergent and computationally efficient. We first develop a general theory for composite optimization problems satisfying specific geometric regularity conditions. \n\nBy establishing a rigorous link between primal quadratic growth and dual quadratic decay, we derive novel error bounds showing that the computable duality gap can serve as a tight proxy for the distance to the solution set. Leveraging this property, we design a restart scheme that upgrades generic sublinear algorithms to achieve provable linear convergence for both primal and dual objectives. We then instantiate this framework for the perspective relaxation of sparse GLMs. \n\nWe prove that standard GLM loss functions and the implicit perspective regularizer satisfy the required geometric conditions. Furthermore, we develop specialized algorithms to evaluate the non-smooth regularizer and its proximal operator exactly in log-linear time, avoiding the high cost of generic conic solvers. Extensive experiments on synthetic and real-world datasets demonstrate that our approach leverages GPU acceleration to speed up dual bound computations by orders of magnitude, significantly enhancing the capability of BnB to certify optimality for large-scale problems.", "occurrence_notes":null, "guid":"144573-21895503@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/144573", "building_id":"1000429", "building_name":"Industrial and Operations Engineering Building", "campus_maps_id":"73", "room":"1680", "location_name":"Industrial and Operations Engineering Building", "has_livestream":0, "cost":"", "tags":["899 Seminar Series","Graduate","Graduate Students","Industrial And Operations Engineering","Michigan Engineering"], "website":"", "sponsors":[ { "group_name":"Industrial & Operations Engineering", "group_id":"3301", "website":"http:\/\/ioe.engin.umich.edu\/" } ], "image_url":"https:\/\/events.umich.edu\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "styled_images":{ "event_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_thumb\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "event_large":"https:\/\/events.umich.edu\/media\/cache\/event_large\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "event_large_2x":"https:\/\/events.umich.edu\/media\/cache\/event_large_2x\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "event_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/event_large_lightbox\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "group_thumb":"https:\/\/events.umich.edu\/media\/cache\/group_thumb\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "group_thumb_square":"https:\/\/events.umich.edu\/media\/cache\/group_thumb_square\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "group_large":"https:\/\/events.umich.edu\/media\/cache\/group_large\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "group_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/group_large_lightbox\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "event_large_crop":"https:\/\/events.umich.edu\/media\/cache\/event_large_crop\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "event_list":"https:\/\/events.umich.edu\/media\/cache\/event_list\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "event_list_2x":"https:\/\/events.umich.edu\/media\/cache\/event_list_2x\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "event_grid":"https:\/\/events.umich.edu\/media\/cache\/event_grid\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "event_grid_2x":"https:\/\/events.umich.edu\/media\/cache\/event_grid_2x\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "event_feature_large":"https:\/\/events.umich.edu\/media\/cache\/event_feature_large\/media\/attachments\/2026\/01\/event_144573_original-1.jpg", "event_feature_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_feature_thumb\/media\/attachments\/2026\/01\/event_144573_original-1.jpg" }, "occurrence_count":1, "first_occurrence":21895503 } , "144903-21896126": { "datetime_modified":"20260202T094257", "datetime_start":"20260212T153000", "datetime_end":"20260212T162000", "has_end_time":1, "date_start":"2026-02-12", "date_end":"2026-02-12", "time_start":"15:30:00", "time_end":"16:20:00", "time_zone":"America\/Detroit", "event_title":"The Department of Astronomy 2025-2026 Colloquium Series Presents:", "occurrence_title":"", "combined_title":"The Department of Astronomy 2025-2026 Colloquium Series Presents:: Dr. Sebastian Heinz, John and Abigail Van Vleck Professor of Astronomy, University of Wisconsin, Madison", "event_subtitle":"Dr. Sebastian Heinz, John and Abigail Van Vleck Professor of Astronomy, University of Wisconsin, Madison", "event_type":"Lecture \/ Discussion", "event_type_id":"13", "description":"\"Shooting for the Stars: Jet-Wind Interactions and their Role in Understanding Jet Physics\"\n\nRelativistic Jets carry vast amounts of energy and magnetic flux from accreting black holes into the interstellar and intergalactic medium. They are routinely invoked as key sources of feedback in structure formation. And yet, after over 60 years of study, the mechanisms through which they couple with their environment, and even their fundamental properties like particle content, velocity, and instantaneous power are still poorly understood. I will discuss a mechanism by which we can shed light on some of the outstanding questions in jet physics: Their interaction with stellar winds, on scales from Galactic X-ray binaries to supermassive black holes in galaxy clusters.", "occurrence_notes":null, "guid":"144903-21896126@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/144903", "building_id":"1000167", "building_name":"West Hall", "campus_maps_id":"163", "room":"411", "location_name":"West Hall", "has_livestream":0, "cost":"", "tags":["astrophysics","astronomy"], "website":"https:\/\/lsa.umich.edu\/astro", "sponsors":[ { "group_name":"Department of Astronomy", "group_id":"1178", "website":"" }, { "group_name":"Department of Physics", "group_id":"1965", "website":"" } ], "image_url":"https:\/\/events.umich.edu\/media\/attachments\/2026\/02\/event_144903_original-1.png", "styled_images":{ "event_thumb":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_thumb\/media\/attachments\/2026\/02\/event_144903_original-1.png", "event_large":"https:\/\/events.umich.edu\/media\/cache\/event_large\/media\/attachments\/2026\/02\/event_144903_original-1.png", "event_large_2x":"https:\/\/events.umich.edu\/media\/cache\/event_large_2x\/media\/attachments\/2026\/02\/event_144903_original-1.png", "event_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/event_large_lightbox\/media\/attachments\/2026\/02\/event_144903_original-1.png", "group_thumb":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_thumb\/media\/attachments\/2026\/02\/event_144903_original-1.png", "group_thumb_square":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_thumb_square\/media\/attachments\/2026\/02\/event_144903_original-1.png", "group_large":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_large\/media\/attachments\/2026\/02\/event_144903_original-1.png", "group_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/group_large_lightbox\/media\/attachments\/2026\/02\/event_144903_original-1.png", "event_large_crop":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_large_crop\/media\/attachments\/2026\/02\/event_144903_original-1.png", "event_list":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_list\/media\/attachments\/2026\/02\/event_144903_original-1.png", "event_list_2x":"https:\/\/events.umich.edu\/media\/cache\/event_list_2x\/media\/attachments\/2026\/02\/event_144903_original-1.png", "event_grid":"https:\/\/events.umich.edu\/media\/cache\/event_grid\/media\/attachments\/2026\/02\/event_144903_original-1.png", "event_grid_2x":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_grid_2x\/media\/attachments\/2026\/02\/event_144903_original-1.png", "event_feature_large":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_feature_large\/media\/attachments\/2026\/02\/event_144903_original-1.png", "event_feature_thumb":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_feature_thumb\/media\/attachments\/2026\/02\/event_144903_original-1.png" }, "occurrence_count":1, "first_occurrence":21896126 } , "144454-21895380": { "datetime_modified":"20260125T201312", "datetime_start":"20260212T154500", "datetime_end":"20260212T170000", "has_end_time":1, "date_start":"2026-02-12", "date_end":"2026-02-12", "time_start":"15:45:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"Algebraic Geometry Learning Seminar: Matroidal families and the main theorem", "occurrence_title":"", "combined_title":"Algebraic Geometry Learning Seminar: Matroidal families and the main theorem: Alex Perry", "event_subtitle":"Alex Perry", "event_type":"Workshop \/ Seminar", "event_type_id":"21", "description":"Discuss the notion of a matroidal family of abelian varieties associated to a regular matroid. 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If you'd like to indicate that you'll be attending this event and see more details, please go to this link: https:\/\/umich.joinhandshake.com\/events\/1903401\/share_preview \n\nWe want to ensure full and equitable participation in our events. If an accessibility accommodation would promote your full participation in this event,\u00a0please indicate your accommodation requirements in this form, preferably at least 14 days prior to the program. If you have any questions regarding access to our programs, please don't hesitate to reach out to Cierra Sutherland at\u00a0cierrasu@umich.edu to ensure sufficient time for arranging your requested accommodation(s) or exploring suitable alternatives. \n\n#UCC", "occurrence_notes":null, "guid":"144875-21896082@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/144875", "building_id":"", "building_name":"", "campus_maps_id":"", "room":"", "location_name":"", "has_livestream":0, "cost":"", "tags":["psip"], "website":"", "sponsors":[ { "group_name":"University Career Center UCC", "group_id":"1140", "website":"http:\/\/careercenter.umich.edu" } ], "image_url":"", "styled_images":{ "event_thumb":"", "event_large":"", "event_large_2x":"", "event_large_lightbox":"", "group_thumb":"", "group_thumb_square":"", "group_large":"", "group_large_lightbox":"", "event_large_crop":"", "event_list":"", "event_list_2x":"", "event_grid":"", "event_grid_2x":"", "event_feature_large":"", "event_feature_thumb":"" }, "occurrence_count":1, "first_occurrence":21896082 } }