{"587037":{"#nid":"587037","#data":{"type":"event","title":"PhD Defense by Jeffrey Pavelka","body":[{"value":"\u003Cp\u003ETitle: Scaling-based Methods in Optimization and Cut Generation\u003C\/p\u003E\r\n\r\n\u003Cp\u003EAdvisor: Dr. Sebastian Pokutta\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003ECommittee Members:\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Chelsea White\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Alejandro Toriello\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Santanu Dey\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Marc Pfetsch (TU Darmstadt)\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDate and time: Thursday, February 16th, 10:00 AM.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003ELocation: ISyE Main Building, room 341.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EAbstract:\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EThis thesis addresses both theoretical and practical concerns in integer programming. In Chapter 2 we discuss scaling-based primal methods for integer programming. Such methods optimize by repeatedly solving augmentation problems - given a polytope, cost vector, and feasible solution, either return a solution with improved objective value or assert that none exists. It is known that with clever scaling of the objective vector,\u0026nbsp;one can optimize by solving only\u0026nbsp;polynomially many augmentation sub-problems. We discuss two known scaling algorithms - bit scaling and geometric scaling - and prove tightened bounds on the number of augmentations necessary. We also explore the practical\u0026nbsp;feasibility of such schemes with a computational study.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EChapter 3\u0026nbsp;addresses questions regarding Chvatal-Gomory (CG) cuts for 0\/1 polytopes. The CG rank of such polytopes is known to be\u0026nbsp;O(n^2\\log(n)) in general. We prove a tighter bound for such polyhedra which, while still O(n^2\\log(n)) in general, implies asymptotically improved bounds for several classes of polyhedra. Furthermore, we address the question of complexity for the separation problem over a family of cuts related to CG cuts, called mod-k cuts. We show this problem to be NP complete.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EFinally, Chapter 4 turns away from integer programming theory, instead focusing on an application in inventory management. We study a scenario (inspired by collaboration with a large online retailer) in which replenishment opportunities arise according to a process outside our control. We devise a stochastic model for use in this scenario, and test its\u0026nbsp;usefulness by way of a simulation study using actual sales data from our collaborator.\u0026nbsp;Of particular interest here is the use of data-driven prediction techniques to tune model parameters. We demonstrate that predictions culled from sophisticated machine learning techniques (e.g.\\ neural network regression) can provide a boost in performance as compared to simpler, classical techniques (e.g.\\ moving averages).\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Scaling-based Methods in Optimization and Cut Generation"}],"uid":"27707","created_gmt":"2017-02-07 12:02:03","changed_gmt":"2017-02-07 12:02:03","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2017-02-16T10:00:00-05:00","event_time_end":"2017-02-16T12:00:00-05:00","event_time_end_last":"2017-02-16T12:00:00-05:00","gmt_time_start":"2017-02-16 15:00:00","gmt_time_end":"2017-02-16 17:00:00","gmt_time_end_last":"2017-02-16 17:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78771","name":"Public"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}