  Motivated by the fact that the gradient-based optimization algorithms can be
studied from the perspective of limiting ordinary differential equations
(ODEs), here we derive an ODE representation of the accelerated triple momentum
(TM) algorithm. For unconstrained optimization problems with strongly convex
cost, the TM algorithm has a proven faster convergence rate than the Nesterov's
accelerated gradient (NAG) method but with the same computational complexity.
We show that similar to the NAG method to capture accurately the
characteristics of the TM method, we need to use a high-resolution modeling to
obtain the ODE representation of the TM algorithm. We use a Lyapunov analysis
to investigate the stability and convergence behavior of the proposed
high-resolution ODE representation of the TM algorithm. We show through this
analysis that this ODE model has robustness to deviation from the parameters of
the TM algorithm. We compare the rate of the ODE representation of the TM
method with that of the NAG method to confirm its faster convergence. Our study
also leads to a tighter bound on the worst rate of convergence for the ODE
model of the NAG method. Lastly, we discuss the use of the integral quadratic
constraint (IQC) method to establish an estimate on the rate of convergence of
the TM algorithm. A numerical example demonstrates our results.
