{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/104952"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/104952","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A new method for projection based model reduction of linear inequality constrained systems","abstract":"Made available in DSpace on 2019-08-23T20:05:25Z (GMT). No. of bitstreams: 2 TURNER-THESIS-2019.pdf: 3096461 bytes, checksum: cc48f6a0078bb1ef676e5ace93e0e9e6 (MD5) LICENSE.txt: 4209 bytes, checksum: c7c4ae4505e7f33fa00504c81837dbf5 (MD5) Previous issue date: 2019-04-26","abstract_html":"Made available in DSpace on 2019-08-23T20:05:25Z (GMT). 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No. of bitstreams: 2 TURNER-THESIS-2019.pdf: 3096461 bytes, checksum: cc48f6a0078bb1ef676e5ace93e0e9e6 (MD5) LICENSE.txt: 4209 bytes, checksum: c7c4ae4505e7f33fa00504c81837dbf5 (MD5) Previous issue date: 2019-04-26","Computational modeling research centers around developing ever better representations of physics. The objective of model reduction specialists is to take that high fidelity understanding and compress it into a Reduced Order Model (ROM) capable of replicating the physical accuracy of the more complicated model with a significantly reduced computational cost. A current challenge in reduced order modeling is the presence of linear inequality constraints in optimization problems. Constrained optimization problems arise in design, contact modeling, financial engineering and other subfields of mathematical modeling. As such, there is a strong motivation to leverage the repeatability of ROMs to rapidly address these engineering challenges. Inherent to the problem of con- strained optimization is feasibility of solutions, and while all FOMs are expected to comply perfectly with their constraints, that property is not necessarily preserved in their corresponding ROMs. The problem is then two fold. First the issue of the constraint must be addressed, and second the resulting ROM must obey the constraints. This thesis develops a method, in a projection-based framework, capable of reducing the linear inequality constraints while preserving a strong degree of feasibility. The proposed method is successfully applied to the reduction of the one-dimensional, constrained Poisson Equation with varied parameters.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-08-22 without embargo terms","The student, Jason Turner, accepted the attached license on 2019-04-26 at 14:52.","The student, Jason Turner, submitted this Thesis for approval on 2019-04-26 at 15:55.","This Thesis was approved for publication on 2019-04-26 at 16:03.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13951 on 2019-08-22 at 14:47:11"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A new method for projection based model reduction of linear inequality constrained systems"]}]}],"canonical_facts":{"dc:contributor":["Balajewicz, Maciej"],"dc:creator":["Turner, Jason Eric"],"dc:date":["2019-08-23T20:05:25Z","2019-04-26","2019-05"],"dc:description":["Made available in DSpace on 2019-08-23T20:05:25Z (GMT). No. of bitstreams: 2 TURNER-THESIS-2019.pdf: 3096461 bytes, checksum: cc48f6a0078bb1ef676e5ace93e0e9e6 (MD5) LICENSE.txt: 4209 bytes, checksum: c7c4ae4505e7f33fa00504c81837dbf5 (MD5) Previous issue date: 2019-04-26","Computational modeling research centers around developing ever better representations of physics. The objective of model reduction specialists is to take that high fidelity understanding and compress it into a Reduced Order Model (ROM) capable of replicating the physical accuracy of the more complicated model with a significantly reduced computational cost. A current challenge in reduced order modeling is the presence of linear inequality constraints in optimization problems. Constrained optimization problems arise in design, contact modeling, financial engineering and other subfields of mathematical modeling. As such, there is a strong motivation to leverage the repeatability of ROMs to rapidly address these engineering challenges. Inherent to the problem of con- strained optimization is feasibility of solutions, and while all FOMs are expected to comply perfectly with their constraints, that property is not necessarily preserved in their corresponding ROMs. The problem is then two fold. First the issue of the constraint must be addressed, and second the resulting ROM must obey the constraints. This thesis develops a method, in a projection-based framework, capable of reducing the linear inequality constraints while preserving a strong degree of feasibility. The proposed method is successfully applied to the reduction of the one-dimensional, constrained Poisson Equation with varied parameters.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-08-22 without embargo terms","The student, Jason Turner, accepted the attached license on 2019-04-26 at 14:52.","The student, Jason Turner, submitted this Thesis for approval on 2019-04-26 at 15:55.","This Thesis was approved for publication on 2019-04-26 at 16:03.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13951 on 2019-08-22 at 14:47:11"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/104952"],"dc:language":["en"],"dc:rights":["Copyright 2019 Jason Turner"],"dc:subject":["Constrained Optimization","Model Reduction","POD","Generalized Coordinate Bounding"],"dc:title":["A new method for projection based model reduction of linear inequality constrained systems"],"dc:type":["text"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:44Z"}