Objetivo "Linear programming has proved to be an invaluable tool both in theory and practice. Semidefinite programming surpasses linear programming in terms of expressivity while remaining tractable. This project proposal investigates the modeling power of linear and semidefinite programming, in the context of combinatorial optimization. Within the emerging framework of extended formulations (EFs), I seek a decisive answer to the following question: Which problems can be modeled by a linear or semidefinite program, when the number of constraints and variables are limited? EFs are based on the idea that one should choose the ""right"" variables to model a problem. By extending the set of variables of a problem by a few carefully chosen variables, the number of constraints can in some cases dramatically decrease, making the problem easier to solve. Despite previous high-quality research, the theory of EFs is still on square one. This project proposal aims at (i) transforming our current zero-dimensional state of knowledge to a truly three-dimensional state of knowledge by pushing the boundaries of EFs in three directions (models, types and problems); (ii) using EFs as a lens on complexity by proving strong consequences of important conjectures such as P != NP, and leveraging strong connections to geometry to make progress on the log-rank conjecture. The proposed methodology is: (i) experiment-aided; (ii) interdisciplinary; (iii) constructive." Ámbito científico natural sciencesmathematicspure mathematicsgeometry Programa(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Tema(s) ERC-CG-2013-PE6 - ERC Consolidator Grant - Computer Science and Informatics Convocatoria de propuestas ERC-2013-CoG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-CG - ERC Consolidator Grants Institución de acogida UNIVERSITE LIBRE DE BRUXELLES Aportación de la UE € 1 455 479,00 Dirección AVENUE FRANKLIN ROOSEVELT 50 1050 Bruxelles / Brussel Bélgica Ver en el mapa Región Région de Bruxelles-Capitale/Brussels Hoofdstedelijk Gewest Région de Bruxelles-Capitale/ Brussels Hoofdstedelijk Gewest Arr. de Bruxelles-Capitale/Arr. Brussel-Hoofdstad Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Anastasios Perimenis (Mr.) Investigador principal Samuel Fiorini (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo UNIVERSITE LIBRE DE BRUXELLES Bélgica Aportación de la UE € 1 455 479,00 Dirección AVENUE FRANKLIN ROOSEVELT 50 1050 Bruxelles / Brussel Ver en el mapa Región Région de Bruxelles-Capitale/Brussels Hoofdstedelijk Gewest Région de Bruxelles-Capitale/ Brussels Hoofdstedelijk Gewest Arr. de Bruxelles-Capitale/Arr. Brussel-Hoofdstad Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Anastasios Perimenis (Mr.) Investigador principal Samuel Fiorini (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos
