Haotian Jiang (Microsoft)- Convex Integer Optimization

Designing and analyzing algorithms for optimization problems is a crucial but challenging task that arises in various fields such as business, science, and engineering. Despite the development of various successful optimization algorithms over the past sixty years, many state-of-the-art algorithms are theoretically far from optimal and ad hoc in nature.

In this talk, I will present a unified toolbox for designing optimization algorithms through the general problem of Convex Integer Optimization, which captures many central problems and challenges in optimization today. Our toolbox has resulted in faster algorithms for fundamental tractable problems and better approximation algorithms for central NP-hard problems. Furthermore, it has revealed new connections between NP-hard and tractable problems which have been studied relatively independently for over half a century. Our work has created avenues for further investigations and applications in other fields of computer science and operations research, such as understanding the security of lattice-based cryptography and creating faster solvers for integer programming. Finally, I will conclude the talk with several future research directions and open problems at the frontier of optimization and related areas.