Final Report Summary - SIPA (Semidefinite Programming with Applications in Statistical Learning) The project has produced several results on classical algorithms for convex optimization, giving intuitive insights on the complexity of these methods and highly efficient techniques to accelerate them. These algorithms have a wide range of applications, first and foremost machine learning which has been the focus of a lot of activity lately. This impact works both ways, as the methods we use to accelerate convex optimization algorithms are clearly statistical in nature and work by studying the sequence of iterates independently of the algorithm itself. We believe this is only a first step in a very promising research direction at the interface of optimization and statistics. On the application front, original and efficient methods have been derived to solve classical combinatorial problems: the phasing problem in diffraction imaging and the seriation problem, which have direct applications in e.g. molecular imaging and DNA sequencing. More direct commercial applications were also discussed, notably on the problem of ranking items based on pairwise preferences, which was formulated as a seriation problem.Overall, ERC funding has allowed us to recruit top students and postdocs. Many of them have found positions in leading universities (Princeton, EPFL, etc), or companies (Amazon, Criteo, etc.).
