{"id":{"repo_id":"gatech","oai_identifier":"oai:repository.gatech.edu:1853/78549"},"canonical_url":"https://search.dev.ndltd.org/etd/gatech/oai:repository.gatech.edu:1853/78549","repository":{"repo_id":"gatech","name":"Georgia Tech","base_url":"https://repository.gatech.edu/server/oai/request"},"display":{"title":"Convexification and Global Optimization of Problems Involving the Euclidean Norm","abstract":"The field of deterministic global optimization has advanced significantly over the last several decades, enabled by the development of new algorithmic techniques and improved computer hardware, and is experiencing a surge of interest. However, global optimization methods for general nonlinear problems are less mature than those for other NP-hard classes of optimization problems, such as mixed-integer linear or quadratic optimization. In this thesis, we study a particularly challenging class of nonconvex optimization problems, characterized by the presence of the Euclidean norm. These problems arise naturally in the context of chemical and statistical physics, but also appear in applications including discrete geometry and operations research, and the question of certifying global optimality remains open even for small instances. We identify the simultaneous elimination of Euclidean and permutational symmetry groups, as well as the convexification of reverse convex sets defined by the Euclidean norm, as two key challenges for global optimization methods, and introduce a benchmark library of instances of this type. Furthermore, we advance the state of the art by developing symmetry elimination and convexification techniques in the context of two problems arising in chemistry and physics and one from location theory. Numerical experiments with the general-purpose global optimization solver BARON indicate that our algorithms accelerate the solution of these problems by up to two orders of magnitude.","abstract_html":"The field of deterministic global optimization has advanced significantly over the last several decades, enabled by the development of new algorithmic techniques and improved computer hardware, and is experiencing a surge of interest. However, global optimization methods for general nonlinear problems are less mature than those for other NP-hard classes of optimization problems, such as mixed-integer linear or quadratic optimization. In this thesis, we study a particularly challenging class of nonconvex optimization problems, characterized by the presence of the Euclidean norm. These problems arise naturally in the context of chemical and statistical physics, but also appear in applications including discrete geometry and operations research, and the question of certifying global optimality remains open even for small instances. We identify the simultaneous elimination of Euclidean and permutational symmetry groups, as well as the convexification of reverse convex sets defined by the Euclidean norm, as two key challenges for global optimization methods, and introduce a benchmark library of instances of this type. Furthermore, we advance the state of the art by developing symmetry elimination and convexification techniques in the context of two problems arising in chemistry and physics and one from location theory. Numerical experiments with the general-purpose global optimization solver BARON indicate that our algorithms accelerate the solution of these problems by up to two orders of magnitude.","abstract_has_math":false,"creators":["Kuznetsov, Anatoliy"],"institution":"Georgia Institute of Technology","degree_name":null,"degree_level":"Doctoral","degree_discipline":null,"degree_department":"Chemical and Biomolecular Engineering","school":null,"contributors":[],"advisors":["Sahinidis, Nikolaos"],"committee_chairs":[],"committee_members":["Scott, Joseph K.","Wilson, Corey J.","Boukouvala, Fani","Skolnick, Jeffrey"],"year":2024,"date_issued":"2024-06-26","date_published":"2024-06-26","updated_at":"2026-07-27T19:50:35Z","subjects":["Global optimization","Simultaneous convexification","Symmetry elimination"],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1853/78549","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Sahinidis, Nikolaos"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Scott, Joseph K.","Wilson, Corey J.","Boukouvala, Fani","Skolnick, Jeffrey"]},{"key":"dc:contributor.department","label":"Department","values":["Chemical and Biomolecular Engineering"]},{"key":"dc:creator","label":"Author","values":["Kuznetsov, Anatoliy"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-08-15T12:28:13Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-08-15T12:28:13Z"]},{"key":"dc:date.issued","label":"Date","values":["2024-06-26"]},{"key":"dc:publisher","label":"Institution","values":["Georgia Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Text"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Global optimization","Simultaneous convexification","Symmetry elimination"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1853/78549"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The field of deterministic global optimization has advanced significantly over the last several decades, enabled by the development of new algorithmic techniques and improved computer hardware, and is experiencing a surge of interest. However, global optimization methods for general nonlinear problems are less mature than those for other NP-hard classes of optimization problems, such as mixed-integer linear or quadratic optimization. In this thesis, we study a particularly challenging class of nonconvex optimization problems, characterized by the presence of the Euclidean norm. These problems arise naturally in the context of chemical and statistical physics, but also appear in applications including discrete geometry and operations research, and the question of certifying global optimality remains open even for small instances. We identify the simultaneous elimination of Euclidean and permutational symmetry groups, as well as the convexification of reverse convex sets defined by the Euclidean norm, as two key challenges for global optimization methods, and introduce a benchmark library of instances of this type. Furthermore, we advance the state of the art by developing symmetry elimination and convexification techniques in the context of two problems arising in chemistry and physics and one from location theory. Numerical experiments with the general-purpose global optimization solver BARON indicate that our algorithms accelerate the solution of these problems by up to two orders of magnitude."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Convexification and Global Optimization of Problems Involving the Euclidean Norm"]}]}],"canonical_facts":{"dc:contributor.advisor":["Sahinidis, Nikolaos"],"dc:contributor.committeemember":["Scott, Joseph K.","Wilson, Corey J.","Boukouvala, Fani","Skolnick, Jeffrey"],"dc:contributor.department":["Chemical and Biomolecular Engineering"],"dc:creator":["Kuznetsov, Anatoliy"],"dc:date.accessioned":["2025-08-15T12:28:13Z"],"dc:date.available":["2025-08-15T12:28:13Z"],"dc:date.issued":["2024-06-26"],"dc:description.abstract":["The field of deterministic global optimization has advanced significantly over the last several decades, enabled by the development of new algorithmic techniques and improved computer hardware, and is experiencing a surge of interest. However, global optimization methods for general nonlinear problems are less mature than those for other NP-hard classes of optimization problems, such as mixed-integer linear or quadratic optimization. In this thesis, we study a particularly challenging class of nonconvex optimization problems, characterized by the presence of the Euclidean norm. These problems arise naturally in the context of chemical and statistical physics, but also appear in applications including discrete geometry and operations research, and the question of certifying global optimality remains open even for small instances. We identify the simultaneous elimination of Euclidean and permutational symmetry groups, as well as the convexification of reverse convex sets defined by the Euclidean norm, as two key challenges for global optimization methods, and introduce a benchmark library of instances of this type. Furthermore, we advance the state of the art by developing symmetry elimination and convexification techniques in the context of two problems arising in chemistry and physics and one from location theory. Numerical experiments with the general-purpose global optimization solver BARON indicate that our algorithms accelerate the solution of these problems by up to two orders of magnitude."],"dc:description.degree":["Ph.D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/1853/78549"],"dc:language.iso":["en_US"],"dc:publisher":["Georgia Institute of Technology"],"dc:subject":["Global optimization","Simultaneous convexification","Symmetry elimination"],"dc:title":["Convexification and Global Optimization of Problems Involving the Euclidean Norm"],"dc:type":["Text"],"thesis:degree_level":["Doctoral"]},"updated_at":"2026-07-27T19:50:35Z"}