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Second-order dynamical systems are important tools for solving optimizationproblems, and most of existing works in this field have focused onunconstrained optimization problems. In this paper, we propose an inertialprimal-dual dynamical system with constant viscous damping and time scaling forthe linear equality constrained convex optimization problem, which consists ofa second-order ODE for the primal variable and a first-order ODE for the dualvariable. When the scaling satisfies certain conditions, we prove itsconvergence property without assuming strong convexity. Even the convergencerate can become exponential when the scaling grows exponentially. We also showthat the obtained convergence property of the dynamical system is preservedunder a small perturbation.

"Second-Order Primal'' + "First-Order Dual'' Dynamical Systems with Time Scaling for Linear Equality Constrained Convex Optimization Problems