Objectif "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." Champ scientifique natural sciencesmathematicspure mathematicsgeometry Programme(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) Thème(s) ERC-CG-2013-PE6 - ERC Consolidator Grant - Computer Science and Informatics Appel à propositions ERC-2013-CoG Voir d’autres projets de cet appel Régime de financement ERC-CG - ERC Consolidator Grants Institution d’accueil UNIVERSITE LIBRE DE BRUXELLES Contribution de l’UE € 1 455 479,00 Adresse AVENUE FRANKLIN ROOSEVELT 50 1050 Bruxelles / Brussel Belgique Voir sur la carte Région Région de Bruxelles-Capitale/Brussels Hoofdstedelijk Gewest Région de Bruxelles-Capitale/ Brussels Hoofdstedelijk Gewest Arr. de Bruxelles-Capitale/Arr. Brussel-Hoofdstad Type d’activité Higher or Secondary Education Establishments Contact administratif Anastasios Perimenis (Mr.) Chercheur principal Samuel Fiorini (Prof.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire UNIVERSITE LIBRE DE BRUXELLES Belgique Contribution de l’UE € 1 455 479,00 Adresse AVENUE FRANKLIN ROOSEVELT 50 1050 Bruxelles / Brussel Voir sur la carte Région Région de Bruxelles-Capitale/Brussels Hoofdstedelijk Gewest Région de Bruxelles-Capitale/ Brussels Hoofdstedelijk Gewest Arr. de Bruxelles-Capitale/Arr. Brussel-Hoofdstad Type d’activité Higher or Secondary Education Establishments Contact administratif Anastasios Perimenis (Mr.) Chercheur principal Samuel Fiorini (Prof.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée
