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In Hilbert space, we propose a family of primal-dual dynamical system foraffine constrained convex optimization problem. Several damping coefficients,time scaling coefficients, and perturbation terms are thus considered. Byconstructing the energy functions, we investigate the convergence rates withdifferent choices of the damping coefficients and time scaling coefficients.Our results extend the inertial dynamical approaches for unconstrained convexoptimization problems to affine constrained convex optimization problems.

Perturbed primal-dual dynamics with damping and time scaling coefficients for affine constrained convex optimization problems