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Frontiers of Extended Formulations

Objective

"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."

Call for proposal

ERC-2013-CoG
See other projects for this call

Funding Scheme

ERC-CG - ERC Consolidator Grants

Host institution

UNIVERSITE LIBRE DE BRUXELLES
Address
Avenue Franklin Roosevelt 50
1050 Bruxelles
Belgium
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 455 479
Principal investigator
Samuel Fiorini (Prof.)
Administrative Contact
Anastasios Perimenis (Mr.)

Beneficiaries (1)

UNIVERSITE LIBRE DE BRUXELLES
Belgium
EU contribution
€ 1 455 479
Address
Avenue Franklin Roosevelt 50
1050 Bruxelles
Activity type
Higher or Secondary Education Establishments
Principal investigator
Samuel Fiorini (Prof.)
Administrative Contact
Anastasios Perimenis (Mr.)