First order optimization methods based on Hessian-driven Nesterov accelerated gradient flow

Long Chen and Hao Luo


arXiv   Bibtex coming soon


A novel dynamical inertial Newton system, which is called
Hessian-driven Nesterov accelerated gradient (H-NAG) flow is
proposed. Convergence of the continuous trajectory are established via
tailored Lyapunov function, and new first-order accelerated
optimization methods are proposed from ODE solvers. It is shown that
(semi-)implicit schemes can always achieve linear rate and explicit
schemes have the optimal(accelerated) rates for convex and strongly
convex objectives. In particular, Nesterov's optimal method is
recovered from an explicit scheme for our H-NAG flow. Furthermore,
accelerated splitting algorithms for composite optimization problems
are also developed.