Project description
Integer programmes to answer open algorithmic questions
Recent projects combined with new ideas have opened the way to obtain advanced results in long-standing open problems in the fields of integer programming and online optimisation. The EU-funded ICOPT project proposes to take advantage and extend techniques from the domain of combinatorial optimisation to address some basic open algorithmic questions in these areas. The project will focus on several targets that present interesting combinatorial characteristics. These problems include questions related to integer programming with bounded subdeterminants, the expressive power of mixed-integer linear formulations, and questions on fundamental combinatorial online problems like the matroid secretary conjecture. Advances derived from the project are likely to significantly contribute to mathematical optimisation and theoretical computer science.
Objective
The goal of this proposal is to leverage and significantly extend techniques from the field of Combinatorial Optimization to address some fundamental open algorithmic questions in other, related areas, namely Integer Programming and Online Optimization. More precisely, we focus on the following three thrusts, which share many combinatorial features:
- Integer programming with bounded subdeterminants.
- Expressive power of mixed-integer linear formulations.
- The matroid secretary conjecture, a key online selection problem.
Recent significant progress, in which the PI played a central role, combined with new ideas, give hope to obtain breakthrough results in these fields. Many of the questions we consider are long-standing open problems in their respective area, and any progress is thus likely to be a significant contribution to Mathematical Optimization and Theoretical Computer Science. However, equally importantly, if progress can be achieved through the suggested methodologies, then this would create intriguing new links between different fields, which was a key driver in the selection of the above research thrusts.
Fields of science
Programme(s)
Funding Scheme
ERC-COG - Consolidator GrantHost institution
8092 Zuerich
Switzerland