{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/162709"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/162709","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Global Non-Convex Optimization with Integer Variables","abstract":"Non-convex optimization refers to the process of solving problems whose objective or constraints are non-convex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often relying on approximate solutions. Bertsimas et al. [1] introduce a novel approach for solving continuous non-convex optimization problems to provable optimality, called the Relaxation Perspectification Technique - Branch and Bound (RPT-BB). In this thesis, we extend the RPT-BB approach to the binary, mixed-binary, integer, and mixed-integer variable domains. We outline a novel branch-and-bound algorithm that makes use of the Relaxation Perspectification Technique (RPT), as well as binary, integer, and eigenvector cuts. We demonstrate the performance of this approach on two representative non-convex problems, as well as two real-world non-convex optimization problems, and we benchmark its performance on BARON and SCIP, two state-of-the-art optimization solvers for non-convex mixed-integer problems. We observe that our algorithm, despite being more general, is able to outperform the state-of-the-art solvers on many problem instances.","abstract_html":"Non-convex optimization refers to the process of solving problems whose objective or constraints are non-convex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often relying on approximate solutions. Bertsimas et al. [1] introduce a novel approach for solving continuous non-convex optimization problems to provable optimality, called the Relaxation Perspectification Technique - Branch and Bound (RPT-BB). In this thesis, we extend the RPT-BB approach to the binary, mixed-binary, integer, and mixed-integer variable domains. We outline a novel branch-and-bound algorithm that makes use of the Relaxation Perspectification Technique (RPT), as well as binary, integer, and eigenvector cuts. We demonstrate the performance of this approach on two representative non-convex problems, as well as two real-world non-convex optimization problems, and we benchmark its performance on BARON and SCIP, two state-of-the-art optimization solvers for non-convex mixed-integer problems. We observe that our algorithm, despite being more general, is able to outperform the state-of-the-art solvers on many problem instances.","abstract_has_math":false,"creators":["Kriezis, Demetrios C."],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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We observe that our algorithm, despite being more general, is able to outperform the state-of-the-art solvers on many problem instances."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.Eng."]},{"key":"dc:title","label":"Title","values":["Global Non-Convex Optimization with Integer Variables"]}]}],"canonical_facts":{"dc:contributor.advisor":["Bertsimas, Dimitris"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Kriezis, Demetrios C."],"dc:date.accessioned":["2025-09-18T14:28:28Z"],"dc:date.available":["2025-09-18T14:28:28Z"],"dc:date.issued":["2025-05"],"dc:description.abstract":["Non-convex optimization refers to the process of solving problems whose objective or constraints are non-convex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often relying on approximate solutions. Bertsimas et al. [1] introduce a novel approach for solving continuous non-convex optimization problems to provable optimality, called the Relaxation Perspectification Technique - Branch and Bound (RPT-BB). In this thesis, we extend the RPT-BB approach to the binary, mixed-binary, integer, and mixed-integer variable domains. We outline a novel branch-and-bound algorithm that makes use of the Relaxation Perspectification Technique (RPT), as well as binary, integer, and eigenvector cuts. We demonstrate the performance of this approach on two representative non-convex problems, as well as two real-world non-convex optimization problems, and we benchmark its performance on BARON and SCIP, two state-of-the-art optimization solvers for non-convex mixed-integer problems. We observe that our algorithm, despite being more general, is able to outperform the state-of-the-art solvers on many problem instances."],"dc:description.degree":["M.Eng."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/162709"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"dc:rights.uri":["https://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Global Non-Convex Optimization with Integer Variables"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Engineering in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:22:04Z"}