Convergence rate of the second order inertia augmented Lagrangian dynamical system for convex optimization problem

In this work, we come up with a continuous-time second order inertial augmented Lagrangian dynamical system with damping function for solving convex optimization problems with affine equality constraints with three variables. The constrained optimization problem can be transformed into unconstrained optimization problem by using the augmented Lagrange function method. By using Lyapunov analysis method, the asymptotic properties of the dynamic system at t → ∞ is studied and the convergence rates are established when the damping coefficients are different situations.