{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/87075"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/87075","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Mixed Integer Nonlinear Programs: Theory, Algorithms and Applications","abstract":"This dissertation develops an efficient solution strategy for finding global optima of continuous, integer, and mixed integer nonlinear programs. The main contributions of this thesis are: (1) We develop the first constructive technique for characterizing convex envelopes of nonlinear functions. Demonstrating the technique, we derive a semidefinite relaxation for fractional programs. In the process, we introduce the concept of convex extensions, study its convexification properties, and apply it to develop tight relaxations for hyperbolic programs and pooling/blending problems. (2) We develop a theoretical framework for range-reduction and provide a unified treatment of existing and new domain reduction techniques. (3) We develop a finite algorithm for two stage stochastic integer programs where earlier approaches were either convergent only in limit (i.e., infinite) or resorted to explicit enumeration. (4) We provide computational experience to demonstrate that our implementation of the proposed algorithms (BARON-NLP) can routinely solve problems previously not amenable to optimization techniques. We characterize the feasible space of a refrigerant design problem proposed 15 years ago and provide new solutions and/or improved computational results with respect to earlier approaches on benchmark problems in stochastic decision making, pooling and blending problems in the petrochemical industry, and restaurant location problems.","abstract_html":"This dissertation develops an efficient solution strategy for finding global optima of continuous, integer, and mixed integer nonlinear programs. The main contributions of this thesis are: (1) We develop the first constructive technique for characterizing convex envelopes of nonlinear functions. Demonstrating the technique, we derive a semidefinite relaxation for fractional programs. In the process, we introduce the concept of convex extensions, study its convexification properties, and apply it to develop tight relaxations for hyperbolic programs and pooling/blending problems. (2) We develop a theoretical framework for range-reduction and provide a unified treatment of existing and new domain reduction techniques. (3) We develop a finite algorithm for two stage stochastic integer programs where earlier approaches were either convergent only in limit (i.e., infinite) or resorted to explicit enumeration. (4) We provide computational experience to demonstrate that our implementation of the proposed algorithms (BARON-NLP) can routinely solve problems previously not amenable to optimization techniques. We characterize the feasible space of a refrigerant design problem proposed 15 years ago and provide new solutions and/or improved computational results with respect to earlier approaches on benchmark problems in stochastic decision making, pooling and blending problems in the petrochemical industry, and restaurant location problems.","abstract_has_math":false,"creators":["Tawarmalani, Mohit"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Industrial Engineering","degree_department":null,"school":null,"contributors":["Sahinidis, Nikolaos V."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:37:15Z","date_published":"2015-09-28T15:37:15Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Computer Science"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3023212"],"render_values":[{"text":"(MiAaPQ)AAI3023212","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/87075","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Sahinidis, Nikolaos V."]},{"key":"dc:creator","label":"Author","values":["Tawarmalani, Mohit"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:37:15Z","10000-01-01","2001"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Industrial Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/87075","(MiAaPQ)AAI3023212"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This dissertation develops an efficient solution strategy for finding global optima of continuous, integer, and mixed integer nonlinear programs. The main contributions of this thesis are: (1) We develop the first constructive technique for characterizing convex envelopes of nonlinear functions. Demonstrating the technique, we derive a semidefinite relaxation for fractional programs. In the process, we introduce the concept of convex extensions, study its convexification properties, and apply it to develop tight relaxations for hyperbolic programs and pooling/blending problems. (2) We develop a theoretical framework for range-reduction and provide a unified treatment of existing and new domain reduction techniques. (3) We develop a finite algorithm for two stage stochastic integer programs where earlier approaches were either convergent only in limit (i.e., infinite) or resorted to explicit enumeration. (4) We provide computational experience to demonstrate that our implementation of the proposed algorithms (BARON-NLP) can routinely solve problems previously not amenable to optimization techniques. We characterize the feasible space of a refrigerant design problem proposed 15 years ago and provide new solutions and/or improved computational results with respect to earlier approaches on benchmark problems in stochastic decision making, pooling and blending problems in the petrochemical industry, and restaurant location problems.","Made available in DSpace on 2015-09-28T15:37:15Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3023212.pdf: 11360956 bytes, checksum: b4d65c9108d297a2e55b2213aebb4fb7 (MD5) Previous issue date: 2001","Embargo set by: Seth Robbins for item 88356 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","257 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001."]},{"key":"dc:title","label":"Title","values":["Mixed Integer Nonlinear Programs: Theory, Algorithms and Applications"]}]}],"canonical_facts":{"dc:contributor":["Sahinidis, Nikolaos V."],"dc:creator":["Tawarmalani, Mohit"],"dc:date":["2015-09-28T15:37:15Z","10000-01-01","2001"],"dc:description":["This dissertation develops an efficient solution strategy for finding global optima of continuous, integer, and mixed integer nonlinear programs. The main contributions of this thesis are: (1) We develop the first constructive technique for characterizing convex envelopes of nonlinear functions. Demonstrating the technique, we derive a semidefinite relaxation for fractional programs. In the process, we introduce the concept of convex extensions, study its convexification properties, and apply it to develop tight relaxations for hyperbolic programs and pooling/blending problems. (2) We develop a theoretical framework for range-reduction and provide a unified treatment of existing and new domain reduction techniques. (3) We develop a finite algorithm for two stage stochastic integer programs where earlier approaches were either convergent only in limit (i.e., infinite) or resorted to explicit enumeration. (4) We provide computational experience to demonstrate that our implementation of the proposed algorithms (BARON-NLP) can routinely solve problems previously not amenable to optimization techniques. We characterize the feasible space of a refrigerant design problem proposed 15 years ago and provide new solutions and/or improved computational results with respect to earlier approaches on benchmark problems in stochastic decision making, pooling and blending problems in the petrochemical industry, and restaurant location problems.","Made available in DSpace on 2015-09-28T15:37:15Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3023212.pdf: 11360956 bytes, checksum: b4d65c9108d297a2e55b2213aebb4fb7 (MD5) Previous issue date: 2001","Embargo set by: Seth Robbins for item 88356 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","257 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001."],"dc:identifier":["http://hdl.handle.net/2142/87075","(MiAaPQ)AAI3023212"],"dc:language":["eng"],"dc:subject":["Computer Science"],"dc:title":["Mixed Integer Nonlinear Programs: Theory, Algorithms and Applications"],"dc:type":["text"],"thesis:degree_discipline":["Industrial Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:28Z"}