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ERC

FOREFRONT Report Summary

Project ID: 615640
Funded under: FP7-IDEAS-ERC
Country: Belgium

Periodic Report Summary 2 - FOREFRONT (Frontiers of Extended Formulations)

The FOREFRONT project (Frontiers of Extended Formulations) investigates the modeling power of linear and semidefinite programming, in the context of combinatorial optimization. Within the emerging framework of extended formulations, it addresses the following question: Which problems can be modeled by a linear or semidefinite program, when the number of constraints and variables are limited?

We aim at answering this question as broadly as possible, without any extra assumption on the model used (such as, restricting to a particular hierarchy).

The project has strong geometric aspects because it seeks to quantify how efficiently we can describe or approximate a given polytope as the projection of a higher-dimensional polyhedron, or spectrahedron. It also has strong ties to (quantum) communication complexity, and approximation algorithms.

The theory of extended formulations offers a lot of exciting challenges, e.g., concerning linear programming approximate extended formulations, and (either exact or approximate) semidefinite programming extended formulations.

Reported by

UNIVERSITE LIBRE DE BRUXELLES
Belgium
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