Tractable quasI-Newton non-smooth Optimization Methods for large scale Data Science – TRINOM-DS

Structured composite non-smooth optimization has proved to be extremely useful in data science, where a common trend is the deluge of large-scale multidimensional data, which drives the need for more efficient optimization schemes. While, so far, primarily, first-order schemes have been widely used to solve such optimization problems, they are quickly approaching their natural (and provable) limitations. In contrast, higher-order methods, in particular quasi-Newton ones, are hardly used due to their lack of scalability, the complexity in their mathematical analysis and the deployment in the non-smooth case. TRINOM-DS will unlock these bottlenecks and develop theoretical, numerical and algorithmic advances to exploit the great potential of quasi-Newton-type schemes for non-smooth large-scale optimization problems, which are ubiquitous in data science. These algorithms will be developed in a variety of challenging settings, and are expected to have far reaching applications in data science, e.g., machine learning (optimal transport, deep learning, etc), imaging and computer vision. They will be implemented as fast optimization codes, possibly on dedicated architectures, that will be made publicly available following the philosophy of reproducible research. TRINOM-DS’s members are very active players in the European school of optimization and data science, which makes this project a unique opportunity to give a scalable, computational and practical embodiment to higher-order non-smooth optimization methods.