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Motivated by the fact that the gradient-based optimization algorithms can bestudied 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 convexcost, the TM algorithm has a proven faster convergence rate than the Nesterov'saccelerated gradient (NAG) method but with the same computational complexity.We show that similar to the NAG method to capture accurately thecharacteristics of the TM method, we need to use a high-resolution modeling toobtain the ODE representation of the TM algorithm. We use a Lyapunov analysisto investigate the stability and convergence behavior of the proposedhigh-resolution ODE representation of the TM algorithm. We show through thisanalysis that this ODE model has robustness to deviation from the parameters ofthe TM algorithm. We compare the rate of the ODE representation of the TMmethod with that of the NAG method to confirm its faster convergence. Our studyalso leads to a tighter bound on the worst rate of convergence for the ODEmodel of the NAG method. Lastly, we discuss the use of the integral quadraticconstraint (IQC) method to establish an estimate on the rate of convergence ofthe TM algorithm. A numerical example demonstrates our results.

High-Resolution Modeling of the Fastest First-Order Optimization Method for Strongly Convex Functions