Continuous Optimization Seminar - Guojun Zhang

Title: Hamiltonian Descent Methods

Abstract: In this talk, I will present a paper on the Hamiltonian descent methods (https://arxiv.org/abs/1809.05042). I will start with a brief introduction on Hamiltonian dynamics from a physicist point of view, and describe the relations between differential equations and descent methods. Differential equations can be considered as the continuous limit of first-order descent methods. By discretizing the differential equations, the authors are able to provide three new first-order descent methods. These methods can achieve linear convergence for a larger set of functions than the usual strongly convex and Lipschitz smooth functions.